Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry
Analysis of PDEs
2019-01-14 v1 Differential Geometry
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 . We obtain as a consequence a Liouville theorem for entire solutions which are approximable by solutions on larger and larger compact domains, and, in particular, for entire solutions: they are either constants or standard bubbles.
Keywords
Cite
@article{arxiv.1901.03646,
title = {Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry},
author = {YanYan Li and Luc Nguyen and Bo Wang},
journal= {arXiv preprint arXiv:1901.03646},
year = {2019}
}