Lipschitz continuity for elliptic free boundary problems with Dini mean oscillation coefficients

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Abstract

We establish local interior Lipschitz continuity of the solutions of a class of free boundary elliptic problems assuming the coefficients of the equation of Dini mean oscillation in at least one direction. The novelty in this regularity result lies in the fact that it allows discontinuous coefficients in all but one variable.

Original languageEnglish
Pages (from-to)57-68
Number of pages12
JournalPortugaliae Mathematica
Volume81
Issue number1-2
DOIs
Publication statusPublished - 2024

Keywords

  • Dini mean oscillation condition
  • free boundary problem
  • Harnack’s inequality
  • Lipschitz continuity

ASJC Scopus subject areas

  • General Mathematics

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