This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Caffarelli, LuisSavin, OvidiuValdinoci, Enrico2016-03-242019-06-282013https://doi.org/10.34657/2669https://oa.tib.eu/renate/handle/123456789/3189We 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.application/pdfeng510Regularity resultsfree boundary problemsmonotonicity formulasPotenzialtheorieDirichletsches IntegralReport