Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry
Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry
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DOI：
10.1007/978-3-030-34953-0_11
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发表时间：
2019-01
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影响因子：
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通讯作者：
Yanyan Li;Luc Nguyen;Bo Wang
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文献类型：
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作者：
Yanyan Li;Luc Nguyen;Bo Wang
本文研究了具有共形Hessian算子的完全非线性椭圆型方程的整体连续粘性解。证明了竞争者之一为C1，1时（非一致）椭圆型方程的强比较原理和Hopf引理。作为结果，我们得到一个刘维尔定理的整体解决方案，这是近似的C1，1解决方案上越来越大的紧凑的域，特别是，整个C1，1 loc解决方案：他们要么是常数或标准泡沫。
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.