JournalsaihpcVol. 32, No. 1pp. 1–22

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

  • Alberto Farina

    Université de Picardie J. Verne, LAMFA, CNRS UMR 7352, Amiens, France

  • Luigi Montoro

    Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31B, I-87036 Arcavacata di Rende, Cosenza, Italy

  • Giuseppe Riey

    Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31B, I-87036 Arcavacata di Rende, Cosenza, Italy

  • Berardino Sciunzi

    Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31B, I-87036 Arcavacata di Rende, Cosenza, Italy
Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces cover
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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 with respect to 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.

Cite this article

Alberto Farina, Luigi Montoro, Giuseppe Riey, Berardino Sciunzi, Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 1–22

DOI 10.1016/J.ANIHPC.2013.09.005