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Minimization of a fractional perimeter-Dirichlet integral functional
2013, Caffarelli, Luis, Savin, Ovidiu, Valdinoci, Enrico
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.