GEOMETRIC PROPERTIES OF SOLUTIONS TO THE ANISOTROPIC p-LAPLACE EQUATION IN DIMENSION TWO

Abstract

We consider solutions to the equation div(|A∇u · ∇u|(p−2)/2A∇u) = 0 with 1 < p < +∞ , A = A(x) a uniformly elliptic and Lipschitz continuous symmetric matrix, in dimension two. We study the properties of critical points and level lines of such solutions and we apply our results to obtain generalizations of a strong comparison principle due to Manfredi and of a univalence theorem by Radó.

Cite this paper

@inproceedings{AlessandriniGEOMETRICPO, title={GEOMETRIC PROPERTIES OF SOLUTIONS TO THE ANISOTROPIC p-LAPLACE EQUATION IN DIMENSION TWO}, author={Giovanni Alessandrini and Mario Sigalotti} }