Liouville theorems on the upper half space

Lei Wang; Meijun Zhu

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arXiv · 1902.05187

Liouville theorems on the upper half space

Lei Wang·Meijun Zhu

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Abstract

In this paper we shall establish some Liouville theorems for solutions bounded from below to certain linear elliptic equations on the upper half space. In particular, we show that for $a \in (0, 1)$ constants are the only $C^1$ up to the boundary positive solutions to $div(x_n^a \nabla u)=0$ on the upper half space.

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Lei Wang, Meijun Zhu. 2019-02-14. Liouville theorems on the upper half space. https://arxiv.org/abs/1902.05187

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