preprint

Inserted: 21 jun 2023
Last Updated: 20 jun 2026

Year: 2023

Abstract:

In this paper, we study the classification of Lipschitz global solutions for a two-phase $p$-Laplace Bernoulli problem. Specifically, we focus on the scenario where the \textit{interior} two-phase points of the global solution are non-empty. Our results show that the expected $C^{1,\eta}$ regularity holds in a suitable neighborhood of certain two-phase points, which we refer to to as \textit{regular} two-phase points.