Regularity results for a free interface problem with Hölder coefficients

We study a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type albeit of very general form allowing the dependence from the unknown variable u and the position x . We employ the regularity theory of Λ -minimizers to study the regularity of t...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 62; no. 5
Main Authors Esposito, L., Lamberti, L.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
Springer Nature B.V
Subjects
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Dirichlet problem
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Regularity
Systems Theory
Theoretical
49N60
49Q10
49Q20
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Summary:We study a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type albeit of very general form allowing the dependence from the unknown variable u and the position x . We employ the regularity theory of Λ -minimizers to study the regularity of the free interface. The hallmark of the paper is the mild regularity assumption concerning the dependence of the coefficients with respect to x and u that is of Hölder type.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02490-x