Global minimizers of the two-phase Bernoulli problem with the p-Laplace operator

Masoud Bayrami; Morteza Fotouhi

doi:10.1007/s00208-026-03533-2

Global minimizers of the two-phase Bernoulli problem with the p-Laplace operator

Masoud Bayrami
, Morteza Fotouhi^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Journal Publication › Article › peer-review

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 interior two-phase points of the global solution are non-empty. Our results show that the expected C1,η regularity holds in a suitable neighborhood of certain two-phase points, which we refer to as regular two-phase points.

Original language	English
Article number	3
Journal	Mathematische Annalen
Volume	396
Issue number	1
DOIs	https://doi.org/10.1007/s00208-026-03533-2
Publication status	Published - Sept 2026

ASJC Scopus subject areas

General Mathematics

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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 interior two-phase points of the global solution are non-empty. Our results show that the expected C1,η regularity holds in a suitable neighborhood of certain two-phase points, which we refer to as regular two-phase points.",

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AB - 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 interior two-phase points of the global solution are non-empty. Our results show that the expected C1,η regularity holds in a suitable neighborhood of certain two-phase points, which we refer to as regular two-phase points.

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Global minimizers of the two-phase Bernoulli problem with the p-Laplace operator

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