Minimization of a fractional perimeter-Dirichlet integral functional
Luis Caffarelli
University of Texas at Austin, Department of Mathematics, 1 University Station, C1200 Austin, TX 78712-1082, USAOvidiu Savin
Columbia University, Mathematics Department, 2990 Broadway, New York, NY 10027, USAEnrico Valdinoci
Weierstraß Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, D-10117 Berlin, Germany
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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 this article
Luis Caffarelli, Ovidiu Savin, Enrico Valdinoci, Minimization of a fractional perimeter-Dirichlet integral functional. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 4, pp. 901–924
DOI 10.1016/J.ANIHPC.2014.04.004