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

Li, Y
Nguyen, L
Wang, B

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.

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