Regularity Results for a free interface problem with Hölder coefficients

2022/10/17 by Esposito, Luca, Lamberti, Lorenzo · 2 citations
#49N60 #49Q10 #49Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2210.09057

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 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.

Cited by

• Ahlfors-regularity for minimizers of a multiphase optimal design problem
• Quantitative regularity properties for the optimal design problem

Related

• Regularity results for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position
• On the regularity of critical and minimal sets of a free interface problem
• Regularity Results for an Optimal Design Problem with lower order terms
• Borderline regularity in singular free boundary problems
• Boundary regularity of the free interface in spectral optimal partition problems