Non-autonomous overdetermined problems for the normalized p-Laplacian

TL;DR

This paper investigates the existence and nonexistence of solutions to overdetermined boundary value problems involving the normalized p-Laplacian, considering a range of p values and non-constant Neumann conditions.

Contribution

It provides new existence and nonexistence results for overdetermined problems with the normalized p-Laplacian, including detailed definitions and boundary conditions.

Findings

Existence results for certain p ranges

Nonexistence results under specific conditions

Analysis of boundary Neumann conditions

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.