Calculus of Variations and Geometric Measure Theory

L. Esposito - L. Lamberti - G. Pisante

Epsilon-regularity for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position

created by lamberti on 02 Jun 2024


Submitted Paper

Inserted: 2 jun 2024
Last Updated: 2 jun 2024

Year: 2024


We establish an ε-regularity result for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by means of an ellipsoidal density that is Hölder continuous with respect to the position variable.

Keywords: free boundary problem, anisotropic surface energies, epsilon-regularity, volume constraint