WIAS Preprint No. 2042, (2014)

A nonlocal free boundary problem


  • Dipierro, Serena
  • Savin, Ovidiu
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35R11 35R35 49Q20 49Q05


  • Fractional perimeter, minimization problem, monotonicity formula, classification of cones




We consider a nonlocal free boundary problem built by a fractional Dirichlet norm plus a fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case. Several classical free boundary problems are limit cases of the one that we consider in this paper.

Appeared in

  • SIAM J. Math. Anal., 47 (2015) pp. 4559--4605.

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