The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds

We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove tha...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Guan, Bo [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions

Übergeordnetes Werk:	Enthalten in: Advances in mathematics - Amsterdam [u.a.] : Elsevier, 1961, 415
Übergeordnetes Werk:	volume:415

DOI / URN:	10.1016/j.aim.2023.108899

Katalog-ID:	ELV065249747

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245	1	0	\|a The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
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520			\|a We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties.
650		4	\|a Fully nonlinear elliptic equations
650		4	\|a Dirichlet problem
650		4	\|a Existence of solutions a priori estimates
650		4	\|a The concavity condition
650		4	\|a Subsolutions
773	0	8	\|i Enthalten in \|t Advances in mathematics \|d Amsterdam [u.a.] : Elsevier, 1961 \|g 415 \|h Online-Ressource \|w (DE-627)268759200 \|w (DE-600)1472893-X \|w (DE-576)103373292 \|x 1090-2082 \|7 nnns
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936	b	k	\|a 31.00 \|j Mathematik: Allgemeines \|q VZ
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allfields	10.1016/j.aim.2023.108899 doi (DE-627)ELV065249747 (ELSEVIER)S0001-8708(23)00042-7 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Guan, Bo verfasserin aut The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties. Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 415 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:415 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 415
spelling	10.1016/j.aim.2023.108899 doi (DE-627)ELV065249747 (ELSEVIER)S0001-8708(23)00042-7 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Guan, Bo verfasserin aut The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties. Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 415 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:415 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 415
allfields_unstemmed	10.1016/j.aim.2023.108899 doi (DE-627)ELV065249747 (ELSEVIER)S0001-8708(23)00042-7 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Guan, Bo verfasserin aut The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties. Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 415 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:415 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 415
allfieldsGer	10.1016/j.aim.2023.108899 doi (DE-627)ELV065249747 (ELSEVIER)S0001-8708(23)00042-7 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Guan, Bo verfasserin aut The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties. Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 415 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:415 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 415
allfieldsSound	10.1016/j.aim.2023.108899 doi (DE-627)ELV065249747 (ELSEVIER)S0001-8708(23)00042-7 DE-627 ger DE-627 rda eng 510 VZ 31.00 bkl Guan, Bo verfasserin aut The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties. Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 415 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:415 GBV_USEFLAG_U GBV_ELV SYSFLAG_U 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_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_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines VZ AR 415
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author	Guan, Bo
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topic_title	510 VZ 31.00 bkl The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds Fully nonlinear elliptic equations Dirichlet problem Existence of solutions a priori estimates The concavity condition Subsolutions
topic	ddc 510 bkl 31.00 misc Fully nonlinear elliptic equations misc Dirichlet problem misc Existence of solutions a priori estimates misc The concavity condition misc Subsolutions
topic_unstemmed	ddc 510 bkl 31.00 misc Fully nonlinear elliptic equations misc Dirichlet problem misc Existence of solutions a priori estimates misc The concavity condition misc Subsolutions
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title	The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
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title_full	The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
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title_sort	the dirichlet problem for fully nonlinear elliptic equations on riemannian manifolds
title_auth	The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
abstract	We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties.
abstractGer	We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties.
abstract_unstemmed	We study the Dirichlet problem for a broad class of fully nonlinear elliptic equations in Euclidean space as well as on general Riemannian manifolds. Under a set of fundamental structure conditions which have become standard since the pioneering work of Cafferalli, Nirenberg and Spruck, we prove that the Dirichlet problem admits a (unique) smooth solution provided that there exists a subsolution. The conditions are essentially optimal, especially with no geometric restrictions to the boundary of the underlying manifold, which is important in applications. We search new ideas and techniques to make use of the concavity condition and subsolution in order to overcome difficulties in deriving key a priori estimates. Along the way we discover some interesting properties of concave functions which should be useful in other fields. Our methods can be adopted to treat other types of fully nonlinear elliptic and parabolic equations on real or complex manifolds. We shall also solve some new equations, which were not covered by previous results even in R n , with interesting properties.
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title_short	The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
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The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds

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