The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains
Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asympto...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Shen, Yan Sheng [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
fractional Poincaré inequality |
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| Anmerkung: |
© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematica sinica - Berlin : Springer, 1985, 39(2023), 11 vom: Nov., Seite 2181-2206 |
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| Übergeordnetes Werk: |
volume:39 ; year:2023 ; number:11 ; month:11 ; pages:2181-2206 |
| Links: |
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| DOI / URN: |
10.1007/s10114-023-2108-8 |
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| Katalog-ID: |
SPR053705246 |
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| 100 | 1 | |a Shen, Yan Sheng |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains |
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| 520 | |a Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. | ||
| 650 | 4 | |a Brezis–Nirenberg problem |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a fractional Poincaré inequality |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a fractional |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -Laplacian |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a unbounded cylinder type domains |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a concentration–compactness principle |7 (dpeaa)DE-He213 | |
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10.1007/s10114-023-2108-8 doi (DE-627)SPR053705246 (SPR)s10114-023-2108-8-e DE-627 ger DE-627 rakwb eng Shen, Yan Sheng verfasserin aut The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. Brezis–Nirenberg problem (dpeaa)DE-He213 fractional Poincaré inequality (dpeaa)DE-He213 fractional (dpeaa)DE-He213 -Laplacian (dpeaa)DE-He213 unbounded cylinder type domains (dpeaa)DE-He213 concentration–compactness principle (dpeaa)DE-He213 Enthalten in Acta mathematica sinica Berlin : Springer, 1985 39(2023), 11 vom: Nov., Seite 2181-2206 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:39 year:2023 number:11 month:11 pages:2181-2206 https://dx.doi.org/10.1007/s10114-023-2108-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 11 11 2181-2206 |
| spelling |
10.1007/s10114-023-2108-8 doi (DE-627)SPR053705246 (SPR)s10114-023-2108-8-e DE-627 ger DE-627 rakwb eng Shen, Yan Sheng verfasserin aut The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. Brezis–Nirenberg problem (dpeaa)DE-He213 fractional Poincaré inequality (dpeaa)DE-He213 fractional (dpeaa)DE-He213 -Laplacian (dpeaa)DE-He213 unbounded cylinder type domains (dpeaa)DE-He213 concentration–compactness principle (dpeaa)DE-He213 Enthalten in Acta mathematica sinica Berlin : Springer, 1985 39(2023), 11 vom: Nov., Seite 2181-2206 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:39 year:2023 number:11 month:11 pages:2181-2206 https://dx.doi.org/10.1007/s10114-023-2108-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 11 11 2181-2206 |
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10.1007/s10114-023-2108-8 doi (DE-627)SPR053705246 (SPR)s10114-023-2108-8-e DE-627 ger DE-627 rakwb eng Shen, Yan Sheng verfasserin aut The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. Brezis–Nirenberg problem (dpeaa)DE-He213 fractional Poincaré inequality (dpeaa)DE-He213 fractional (dpeaa)DE-He213 -Laplacian (dpeaa)DE-He213 unbounded cylinder type domains (dpeaa)DE-He213 concentration–compactness principle (dpeaa)DE-He213 Enthalten in Acta mathematica sinica Berlin : Springer, 1985 39(2023), 11 vom: Nov., Seite 2181-2206 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:39 year:2023 number:11 month:11 pages:2181-2206 https://dx.doi.org/10.1007/s10114-023-2108-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 11 11 2181-2206 |
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10.1007/s10114-023-2108-8 doi (DE-627)SPR053705246 (SPR)s10114-023-2108-8-e DE-627 ger DE-627 rakwb eng Shen, Yan Sheng verfasserin aut The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. Brezis–Nirenberg problem (dpeaa)DE-He213 fractional Poincaré inequality (dpeaa)DE-He213 fractional (dpeaa)DE-He213 -Laplacian (dpeaa)DE-He213 unbounded cylinder type domains (dpeaa)DE-He213 concentration–compactness principle (dpeaa)DE-He213 Enthalten in Acta mathematica sinica Berlin : Springer, 1985 39(2023), 11 vom: Nov., Seite 2181-2206 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:39 year:2023 number:11 month:11 pages:2181-2206 https://dx.doi.org/10.1007/s10114-023-2108-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 11 11 2181-2206 |
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10.1007/s10114-023-2108-8 doi (DE-627)SPR053705246 (SPR)s10114-023-2108-8-e DE-627 ger DE-627 rakwb eng Shen, Yan Sheng verfasserin aut The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. Brezis–Nirenberg problem (dpeaa)DE-He213 fractional Poincaré inequality (dpeaa)DE-He213 fractional (dpeaa)DE-He213 -Laplacian (dpeaa)DE-He213 unbounded cylinder type domains (dpeaa)DE-He213 concentration–compactness principle (dpeaa)DE-He213 Enthalten in Acta mathematica sinica Berlin : Springer, 1985 39(2023), 11 vom: Nov., Seite 2181-2206 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:39 year:2023 number:11 month:11 pages:2181-2206 https://dx.doi.org/10.1007/s10114-023-2108-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 11 11 2181-2206 |
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Shen, Yan Sheng |
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Shen, Yan Sheng misc Brezis–Nirenberg problem misc fractional Poincaré inequality misc fractional misc -Laplacian misc unbounded cylinder type domains misc concentration–compactness principle The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains |
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The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains Brezis–Nirenberg problem (dpeaa)DE-He213 fractional Poincaré inequality (dpeaa)DE-He213 fractional (dpeaa)DE-He213 -Laplacian (dpeaa)DE-He213 unbounded cylinder type domains (dpeaa)DE-He213 concentration–compactness principle (dpeaa)DE-He213 |
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The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains |
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brezis–nirenberg problem for the fractional p-laplacian in unbounded domains |
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The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains |
| abstract |
Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 |
| abstractGer |
Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 |
| abstract_unstemmed |
Abstract In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue %${\lambda _{p,s}}(\widehat {{\omega _\delta }})%$ with respect to the domain %$(\widehat {{\omega _\delta }})%$. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional p-Laplacian setting. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023 |
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The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains |
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https://dx.doi.org/10.1007/s10114-023-2108-8 |
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10.1007/s10114-023-2108-8 |
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