Non-autonomous overdetermined problems for the normalized p-Laplacian

Abstract

We present existence and nonexistence results on the solution of an overdetermined problem for the normalized p-Laplacian in a bounded open set, with p ranging from 1 to infinity. More precisely we consider a non-constant Neumann condition at the boundary. The definitions and statements needed to understand the main results are recalled in detail.

13 pages, 1 figure, statements rephrased, typos corrected, references rearranged