Liouville type theorem for a class of quasilinear p-Laplace type equations in the half space

Abstract

We use the method of vector fields to obtain a Liouville-type theorem for a class of quasilinear p-Laplace type equations with conormal boundary condition in the half space. These p-Laplace type equations are the subcritical case of the Euler-Lagrange equation of the Sobolev trace inequality in the half space.