Minimization of a fractional perimeter-Dirichlet integral functional

Luis Caffarelli, Ovidiu Savin, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely (Formula presented.), with σ ∈ (0,1). We obtain regularity results for the minimizers and for their free boundaries ∂{u>0} using blow-up analysis. We will also give related results about density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.

Original languageEnglish
Pages (from-to)901-924
Number of pages24
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number4
Publication statusPublished - 1 Jul 2015
Externally publishedYes


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