Minimization of a fractional perimeter-Dirichlet integral functional
Analysis of PDEs
2013-06-25 v1
Abstract
We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely with . We obtain regularity results for the minimizers and for their free boundaries using blow-up analysis. We will also give related results about density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.
Cite
@article{arxiv.1306.5337,
title = {Minimization of a fractional perimeter-Dirichlet integral functional},
author = {Luis Caffarelli and Ovidiu Savin and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1306.5337},
year = {2013}
}