Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry

Yan Yan Li; Luc Nguyen; Bo Wang

doi:10.1007/978-3-030-34953-0_11

Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry

Yan Yan Li^*, Luc Nguyen, Bo Wang

^*此作品的通讯作者

数学学院

科研成果: 书/报告/会议事项章节 › 章节 › 同行评审

4 引用（Scopus）

摘要

We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is C1,1. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by C1,1 solutions on larger and larger compact domains, and, in particular, for entire C1,1 loc solutions: they are either constants or standard bubbles.

源语言	英语
主期刊名	Progress in Mathematics
出版商	Birkhauser
页	221-244
页数	24
DOI	https://doi.org/10.1007/978-3-030-34953-0_11
出版状态	已出版 - 2020

出版系列

姓名	Progress in Mathematics
卷	333
ISSN（印刷版）	0743-1643
ISSN（电子版）	2296-505X

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10.1007/978-3-030-34953-0_11

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引用此

Li, Y. Y., Nguyen, L., & Wang, B. (2020). Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry. 在 Progress in Mathematics (页码 221-244). (Progress in Mathematics; 卷 333). Birkhauser. https://doi.org/10.1007/978-3-030-34953-0_11

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abstract = "We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is C1,1. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by C1,1 solutions on larger and larger compact domains, and, in particular, for entire C1,1 loc solutions: they are either constants or standard bubbles.",

keywords = "Hopf Lemma, Liouville theorem, Primary 35J60, Secondary 35J70, conformal geometry, strong comparison principle, viscosity solution",

author = "Li, {Yan Yan} and Luc Nguyen and Bo Wang",

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AU - Li, Yan Yan

AU - Nguyen, Luc

AU - Wang, Bo

PY - 2020

Y1 - 2020

N2 - We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is C1,1. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by C1,1 solutions on larger and larger compact domains, and, in particular, for entire C1,1 loc solutions: they are either constants or standard bubbles.

AB - We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is C1,1. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by C1,1 solutions on larger and larger compact domains, and, in particular, for entire C1,1 loc solutions: they are either constants or standard bubbles.

KW - Hopf Lemma

KW - Liouville theorem

KW - Primary 35J60

KW - Secondary 35J70

KW - conformal geometry

KW - strong comparison principle

KW - viscosity solution

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T3 - Progress in Mathematics

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EP - 244

BT - Progress in Mathematics

PB - Birkhauser

ER -

Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry

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