Some remarks on sign changing solutions of a quasilinear elliptic equation in two variables

Abstract

We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions; the boundary data is assumed to have finite number of relative maximum and minimum values. We are interested in certain vanishing properties of sign changing solutions to such a Dirichlet problem. Our method is applicable in the plane.Comment: In v2, we discuss and fix a gap that was found in our method. However, our results are weaker after this modification. Can be considered part II of arXiv:1205.0785, with which it overlap