Continuity and density results for a one-phase nonlocal free boundary problem
Analysis of PDEs
2016-10-28 v4
Abstract
We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are H\"older continuous and the free boundary has positive density from both sides. For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.
Cite
@article{arxiv.1504.05569,
title = {Continuity and density results for a one-phase nonlocal free boundary problem},
author = {Serena Dipierro and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1504.05569},
year = {2016}
}
Comments
To appear in Annales de l'Institut Henri Poincar\'e Analyse Non Lin\'eaire