Calculus of Variations and Geometric Measure Theory

S. Guarino Lo Bianco - D. A. La Manna - B. Velichkov

A two-phase problem with Robin conditions on the free boundary

created by guarinolo on 31 Mar 2020
modified by velichkov on 02 Jan 2023


Published Paper

Inserted: 31 mar 2020
Last Updated: 2 jan 2023

Journal: Journal de l'École polytechnique - Mathématiques
Year: 2020

ArXiv: 2003.14139 PDF


We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers.