Regularity Results for a free interface problem with Hölder coefficients
Luca Esposito, Lamberti, Lorenzo · arXiv (Cornell University) · 2022
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.