Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry

Author: 

Li, Y
Nguyen, L
Wang, B

Publication Date: 

1 January 2019

Journal: 

Geometric Analysis: In Honor of Gang Tian's 60th Birthday

Last Updated: 

2020-06-26T18:47:45.007+01:00

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 $C^{1,1}$. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by $C^{1,1}$ solutions on larger and larger compact domains, and, in particular, for entire $C^{1,1}_{\rm loc}$ solutions: they are either constants or standard bubbles.

Symplectic id: 

1004696

Submitted to ORA: 

Submitted

Publication Type: 

Chapter