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

Yan Yan Li, Luc Nguyen, Bo Wang

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherBirkhauser
Pages221-244
Number of pages24
DOIs
StatePublished - 2020
Externally publishedYes

Publication series

NameProgress in Mathematics
Volume333
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Hopf Lemma
  • Liouville theorem
  • Primary 35J60
  • Secondary 35J70
  • conformal geometry
  • strong comparison principle
  • viscosity solution

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