WIAS Preprint No. 1818, (2013)

Minimization of a fractional perimeter-Dirichlet integral functional


  • Caffarelli, Luis
  • Savin, Ovidiu
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35B65 49Q05 31A05 49Q15


  • regularity results, free boundary problems, monotonicity formulas


We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set. We obtain regularity results for the minimizers and for their free boundaries using blow-up analysis, density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.

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