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arXiv · 1705.04426

Liouville's theorem and comparison results for solutions of degenerate elliptic equations in exterior domains

Leonardo Prange Bonorino·Andre Rodrigues Silva·Paulo Ricardo de Avila Zingano
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Abstract

A version of Liouville's theorem is proved for solutions of some degenerate elliptic equations defined in $\mathbb{R}^n\backslash K$, where $K$ is a compact set, provided the structure of this equation and the dimension $n$ are related. This result is a correction of a previous one established by Serrin, since some additional hypotheses are necessary. Theoretical and numerical examples are given. Furthermore, a comparison result and the uniqueness of solution are obtained for such equations in exterior domains.

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Leonardo Prange Bonorino, Andre Rodrigues Silva, Paulo Ricardo de Avila Zingano. 2017-05-12. Liouville's theorem and comparison results for solutions of degenerate elliptic equations in exterior domains. https://doi.org/10.1016/j.jmaa.2018.03.046

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