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arXiv · 2210.09057

Regularity Results for a free interface problem with H\"{o}lder coefficients

Luca Esposito·Lorenzo Lamberti
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Abstract

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 $\Lambda$-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 H\"{o}lder type.

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Luca Esposito, Lorenzo Lamberti. 2022-10-17. Regularity Results for a free interface problem with H\"{o}lder coefficients. https://arxiv.org/abs/2210.09057

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