C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations

We establish the interior C 1 , α -estimate for viscosity solutions of de...
Ausführliche Beschreibung

We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = | D u | γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + | D u | 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Lee, Ki-Ahm [verfasserIn] Lee, Se-Chan [verfasserIn] Yun, Hyungsung [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations

Übergeordnetes Werk:	Enthalten in: No title available - 181, Seite 152-189
Übergeordnetes Werk:	volume:181 ; pages:152-189

DOI / URN:	10.1016/j.matpur.2023.12.002

Katalog-ID:	ELV066425387

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100	1		\|a Lee, Ki-Ahm \|e verfasserin \|4 aut
245	1	0	\|a C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
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520			\|a We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient.
650		4	\|a Regularity
650		4	\|a Fully nonlinear equations
650		4	\|a Degenerate parabolic equations
650		4	\|a Singular parabolic equations
700	1		\|a Lee, Se-Chan \|e verfasserin \|4 aut
700	1		\|a Yun, Hyungsung \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t No title available \|g 181, Seite 152-189 \|w (DE-627)271180730 \|x 0021-7824 \|7 nnns
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912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
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_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
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912			\|a GBV_ILN_2007
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912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
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912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
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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allfields	10.1016/j.matpur.2023.12.002 doi (DE-627)ELV066425387 (ELSEVIER)S0021-7824(23)00153-8 DE-627 ger DE-627 rda eng Lee, Ki-Ahm verfasserin aut C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient. Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations Lee, Se-Chan verfasserin aut Yun, Hyungsung verfasserin aut Enthalten in No title available 181, Seite 152-189 (DE-627)271180730 0021-7824 nnns volume:181 pages:152-189 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 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 AR 181 152-189
spelling	10.1016/j.matpur.2023.12.002 doi (DE-627)ELV066425387 (ELSEVIER)S0021-7824(23)00153-8 DE-627 ger DE-627 rda eng Lee, Ki-Ahm verfasserin aut C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient. Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations Lee, Se-Chan verfasserin aut Yun, Hyungsung verfasserin aut Enthalten in No title available 181, Seite 152-189 (DE-627)271180730 0021-7824 nnns volume:181 pages:152-189 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 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 AR 181 152-189
allfields_unstemmed	10.1016/j.matpur.2023.12.002 doi (DE-627)ELV066425387 (ELSEVIER)S0021-7824(23)00153-8 DE-627 ger DE-627 rda eng Lee, Ki-Ahm verfasserin aut C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient. Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations Lee, Se-Chan verfasserin aut Yun, Hyungsung verfasserin aut Enthalten in No title available 181, Seite 152-189 (DE-627)271180730 0021-7824 nnns volume:181 pages:152-189 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 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 AR 181 152-189
allfieldsGer	10.1016/j.matpur.2023.12.002 doi (DE-627)ELV066425387 (ELSEVIER)S0021-7824(23)00153-8 DE-627 ger DE-627 rda eng Lee, Ki-Ahm verfasserin aut C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient. Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations Lee, Se-Chan verfasserin aut Yun, Hyungsung verfasserin aut Enthalten in No title available 181, Seite 152-189 (DE-627)271180730 0021-7824 nnns volume:181 pages:152-189 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 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 AR 181 152-189
allfieldsSound	10.1016/j.matpur.2023.12.002 doi (DE-627)ELV066425387 (ELSEVIER)S0021-7824(23)00153-8 DE-627 ger DE-627 rda eng Lee, Ki-Ahm verfasserin aut C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient. Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations Lee, Se-Chan verfasserin aut Yun, Hyungsung verfasserin aut Enthalten in No title available 181, Seite 152-189 (DE-627)271180730 0021-7824 nnns volume:181 pages:152-189 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 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 AR 181 152-189
language	English
source	Enthalten in No title available 181, Seite 152-189 volume:181 pages:152-189
sourceStr	Enthalten in No title available 181, Seite 152-189 volume:181 pages:152-189
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author	Lee, Ki-Ahm
spellingShingle	Lee, Ki-Ahm misc Regularity misc Fully nonlinear equations misc Degenerate parabolic equations misc Singular parabolic equations C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
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topic_title	C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations Regularity Fully nonlinear equations Degenerate parabolic equations Singular parabolic equations
topic	misc Regularity misc Fully nonlinear equations misc Degenerate parabolic equations misc Singular parabolic equations
topic_unstemmed	misc Regularity misc Fully nonlinear equations misc Degenerate parabolic equations misc Singular parabolic equations
topic_browse	misc Regularity misc Fully nonlinear equations misc Degenerate parabolic equations misc Singular parabolic equations
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
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title_full	C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
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author-letter	Lee, Ki-Ahm
doi_str_mv	10.1016/j.matpur.2023.12.002
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title_sort	c 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
title_auth	C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
abstract	We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient.
abstractGer	We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient.
abstract_unstemmed	We establish the interior C 1 , α -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations u t = \| D u \| γ F ( D 2 u ) + f in Q 1 , where γ > − 1 and f ∈ C ( Q 1 ) ∩ L ∞ ( Q 1 ) . For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . Our approach utilizes the Bernstein method with approximations in view of the difference quotient.
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title_short	C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations
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author2	Lee, Se-Chan Yun, Hyungsung
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doi_str	10.1016/j.matpur.2023.12.002
up_date	2024-07-06T17:42:55.115Z
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For this purpose, we prove the well-posedness of the regularized Cauchy-Dirichlet problem { u t = ( 1 + \| D u \| 2 ) γ / 2 F ( D 2 u ) in Q 1 u = φ on ∂ p Q 1 , where γ > − 2 . 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C 1, -regularity for solutions of degenerate/singular fully nonlinear parabolic equations

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