English

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 \Omu(x)2dx+\Per({u>0},\Om), \int_\Om |\nabla u(x)|^2\,dx+\Per\Big(\{u > 0\},\Om \Big), with σ(0,1)\sigma\in(0,1). We obtain regularity results for the minimizers and for their free boundaries \p{u>0}\p \{u>0\} using blow-up analysis. We will also give related results about density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.

Keywords

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}
}
R2 v1 2026-06-22T00:38:35.434Z