标题： 两相伯努利问题的全局极小值与$p$-拉普拉斯算子 显示英文标题

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

摘要： 在本文中，我们研究了在适度假设下的两相$p$-Laplace Bernoulli 问题的 Lipschitz 全局解的分类。 具体而言，我们关注全局解的内部两相点非空的情况。 我们的结果表明，在某些称为正则两相点的两相点的适当邻域内，预期的$C^{1,\eta}$正则性成立。 显示英文摘要

摘要： In this paper, we study the classification of Lipschitz global solutions for a two-phase $p$-Laplace Bernoulli problem, subject to a mild assumption. 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 $C^{1,\eta}$ regularity holds in a suitable neighborhood of certain two-phase points referred to as regular two-phase points.