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arXiv · 2306.04656

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

Masoud Bayrami-Aminlouee·Morteza Fotouhi
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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 \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.

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Masoud Bayrami-Aminlouee, Morteza Fotouhi. 2023-05-19. Global minimizers of the two-phase Bernoulli problem with the $p$-Laplace operator. https://arxiv.org/abs/2306.04656

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