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<p>We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and Hölder-continuous boundary data. As an application, we use them to extend recent generic uniqueness and regularity results to families of continuous functions.</p>

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Continuity up to the boundary for minimizers of the one-phase Bernoulli problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月27日

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  • Xavier Fernández-Real,
  • Florian Gruen

摘要

We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and Hölder-continuous boundary data. As an application, we use them to extend recent generic uniqueness and regularity results to families of continuous functions.