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

2013/06/03 by Farina, Alberto, Montoro, Luigi, Riey, Giuseppe +1 · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.0381

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.

Cited by

• Monotonicity and Liouville-type theorems for semilinear elliptic problems in the half space
• Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient
• Boundary estimates for singular elliptic problems involving a gradient term

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• Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient