Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces
Analysis of PDEs
2013-06-04 v1
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.
Keywords
Cite
@article{arxiv.1306.0381,
title = {Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces},
author = {Alberto Farina and Luigi Montoro and Giuseppe Riey and Berardino Sciunzi},
journal= {arXiv preprint arXiv:1306.0381},
year = {2013}
}