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arXiv · 1306.0381

Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces

Alberto Farina·Luigi Montoro·Giuseppe Riey·Berardino Sciunzi
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Abstract

We consider a quasilinear elliptic equation involving a first order term, under zero Dirichlet boundary condition in half spaces. We prove that any positive solution is monotone increasing w.r.t. the direction orthogonal to the boundary. The main ingredient in the proof is a new comparison principle in unbounded domains. As a consequence of our analysis, we also obtain some new Liouville type theorems.

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Alberto Farina, Luigi Montoro, Giuseppe Riey, Berardino Sciunzi. 2013-06-03. Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces. https://arxiv.org/abs/1306.0381

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