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arXiv · 1901.03646

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

YanYan Li·Luc Nguyen·Bo Wang
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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 $C^{1,1}$. 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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YanYan Li, Luc Nguyen, Bo Wang. 2019-01-11. Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry. https://arxiv.org/abs/1901.03646

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