Non-compact embeddings of Sobolev spaces

The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip.

Gespeichert in:

Autor*in:	Edmunds, D.E. [verfasserIn] Lang, J. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers

Übergeordnetes Werk:	Enthalten in: Journal of approximation theory - Amsterdam [u.a.] : Elsevier, 1968, 286
Übergeordnetes Werk:	volume:286

DOI / URN:	10.1016/j.jat.2022.105848

Katalog-ID:	ELV00901876X

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520			\|a The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip.
650		4	\|a Sobolev embedding
650		4	\|a Non-compact map
650		4	\|a Strictly singular map
650		4	\|a Finitely strictly singular map
650		4	\|a Bernstein numbers
700	1		\|a Lang, J. \|e verfasserin \|0 (orcid)0000-0003-1582-7273 \|4 aut
773	0	8	\|i Enthalten in \|t Journal of approximation theory \|d Amsterdam [u.a.] : Elsevier, 1968 \|g 286 \|h Online-Ressource \|w (DE-627)266890598 \|w (DE-600)1468964-9 \|w (DE-576)103373136 \|7 nnns
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912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_224
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
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936	b	k	\|a 31.40 \|j Analysis: Allgemeines
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952			\|d 286

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author_variant	d e de j l jl
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publishDate	2022
allfields	10.1016/j.jat.2022.105848 doi (DE-627)ELV00901876X (ELSEVIER)S0021-9045(22)00120-4 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Edmunds, D.E. verfasserin aut Non-compact embeddings of Sobolev spaces 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip. Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers Lang, J. verfasserin (orcid)0000-0003-1582-7273 aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 286 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:286 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 286
spelling	10.1016/j.jat.2022.105848 doi (DE-627)ELV00901876X (ELSEVIER)S0021-9045(22)00120-4 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Edmunds, D.E. verfasserin aut Non-compact embeddings of Sobolev spaces 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip. Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers Lang, J. verfasserin (orcid)0000-0003-1582-7273 aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 286 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:286 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 286
allfields_unstemmed	10.1016/j.jat.2022.105848 doi (DE-627)ELV00901876X (ELSEVIER)S0021-9045(22)00120-4 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Edmunds, D.E. verfasserin aut Non-compact embeddings of Sobolev spaces 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip. Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers Lang, J. verfasserin (orcid)0000-0003-1582-7273 aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 286 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:286 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 286
allfieldsGer	10.1016/j.jat.2022.105848 doi (DE-627)ELV00901876X (ELSEVIER)S0021-9045(22)00120-4 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Edmunds, D.E. verfasserin aut Non-compact embeddings of Sobolev spaces 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip. Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers Lang, J. verfasserin (orcid)0000-0003-1582-7273 aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 286 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:286 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 286
allfieldsSound	10.1016/j.jat.2022.105848 doi (DE-627)ELV00901876X (ELSEVIER)S0021-9045(22)00120-4 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Edmunds, D.E. verfasserin aut Non-compact embeddings of Sobolev spaces 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip. Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers Lang, J. verfasserin (orcid)0000-0003-1582-7273 aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 286 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:286 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 286
language	English
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topic_facet	Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers
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author	Edmunds, D.E.
spellingShingle	Edmunds, D.E. ddc 510 bkl 31.40 misc Sobolev embedding misc Non-compact map misc Strictly singular map misc Finitely strictly singular map misc Bernstein numbers Non-compact embeddings of Sobolev spaces
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topic_title	510 DE-600 31.40 bkl Non-compact embeddings of Sobolev spaces Sobolev embedding Non-compact map Strictly singular map Finitely strictly singular map Bernstein numbers
topic	ddc 510 bkl 31.40 misc Sobolev embedding misc Non-compact map misc Strictly singular map misc Finitely strictly singular map misc Bernstein numbers
topic_unstemmed	ddc 510 bkl 31.40 misc Sobolev embedding misc Non-compact map misc Strictly singular map misc Finitely strictly singular map misc Bernstein numbers
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title	Non-compact embeddings of Sobolev spaces
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title_full	Non-compact embeddings of Sobolev spaces
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title_sort	non-compact embeddings of sobolev spaces
title_auth	Non-compact embeddings of Sobolev spaces
abstract	The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip.
abstractGer	The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip.
abstract_unstemmed	The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip.
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title_short	Non-compact embeddings of Sobolev spaces
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doi_str	10.1016/j.jat.2022.105848
up_date	2024-07-06T21:42:21.578Z
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Non-compact embeddings of Sobolev spaces

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