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- W2595100654 abstract "Given $s,sigmain(0,1)$ and a bounded domain $Omegasubsetmathbb{R}^n$, we consider the following minimization problem of $s$-Dirichlet--plus--$sigma$-perimeter-type $ [u]_{ H^s(mathbb{R}^{2n}setminus(Omega^c)^2) } + {rm Per}_sigma ({u>0},Omega),$ where $[ cdot]_{H^s}$ is the fractional Gagliardo seminorm and ${rm Per}_sigma$ is the 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. The classical free boundary problems are limit cases of the one that we consider in this paper, as $snearrow1$, $sigmanearrow1$, or $sigmasearrow0$." @default.
- W2595100654 created "2017-03-23" @default.
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- W2595100654 date "2014-12-29" @default.
- W2595100654 modified "2023-10-16" @default.
- W2595100654 title "A nonlocal free boundary problem" @default.
- W2595100654 hasPublicationYear "2014" @default.
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