A Strong Maximum Principle and a Compact Support Principle for infinity Laplacian

Anup Biswas

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arXiv · 2012.08416

A Strong Maximum Principle and a Compact Support Principle for infinity Laplacian

Anup Biswas

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Abstract

In this article we find necessary and sufficient conditions for the strong maximum principle and compact support principle for non-negative solutions to the quasilinear elliptic inequalities $$\Delta_\infty u + G(|Du|) - f(u)\,\leq 0\quad \text{in}\; \mathcal{O},$$ and $$\Delta_\infty u + G(|Du|) - f(u)\,\geq 0\quad \text{in}\; \mathcal{O},$$ where $\mathcal{O}$ denotes the infinity Laplacian, $G$ is an appropriate continuous function and $f$ is a nondecreasing, continuous function with $f(0)=0$.

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Anup Biswas. 2020-12-15. A Strong Maximum Principle and a Compact Support Principle for infinity Laplacian. https://arxiv.org/abs/2012.08416

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