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arXiv · 1210.1710

Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces

Alberto Farina·Luigi Montoro·Berardino Sciunzi
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Abstract

We prove a weak comparison principle in narrow unbounded domains for solutions to $-Δ_p u=f(u)$ in the case $2 2$ and $f(\cdot)$ is super-linear. We exploit it to prove the monotonicity of positive solutions to $-Δ_p u=f(u)$ in half spaces (with zero Dirichlet assumption) and therefore to prove some Liouville-type theorems.

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Alberto Farina, Luigi Montoro, Berardino Sciunzi. 2012-10-05. Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces. https://arxiv.org/abs/1210.1710

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