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<p>In this paper, we study the classification of Lipschitz global solutions for a two-phase <i>p</i>-Laplace Bernoulli problem. Specifically, we focus on the scenario where the <i>interior</i> two-phase points of the global solution are non-empty. Our results show that the expected <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^{1,\eta }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>η</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> regularity holds in a suitable neighborhood of certain two-phase points, which we refer to as <i>regular</i> two-phase points.</p>

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

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Masoud Bayrami,
  • Morteza Fotouhi

摘要

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 \(C^{1,\eta }\) C 1 , η regularity holds in a suitable neighborhood of certain two-phase points, which we refer to as regular two-phase points.