دورية أكاديمية
A Nonlocal Free Boundary Problem
| العنوان: | A Nonlocal Free Boundary Problem |
|---|---|
| المؤلفون: | Savin, Ovidiu, Dipierro, Serena, Valdinoci, Enrico |
| سنة النشر: | 2015 |
| المجموعة: | Weierstrass Institute for Applied Analysis and Stochastics publication server |
| مصطلحات موضوعية: | article, ddc:510, Fractional perimeter -- minimization problem -- monotonicity formula -- classification of cones |
| الوصف: | Given $s,\sigma\in(0,1)$ and a bounded domain $\Omega\subset\mathbb{R}^n$, 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 $s\nearrow1$, $\sigma\nearrow1$, or $\sigma\searrow0$. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | SIAM Journal on Mathematical Analysis -- 1095-7154 -- 0036-1410; https://doi.org/10.1137/140999712Test; https://archive.wias-berlin.de/receive/wias_mods_00005810Test |
| DOI: | 10.1137/140999712 |
| الإتاحة: | https://doi.org/10.1137/140999712Test https://archive.wias-berlin.de/receive/wias_mods_00005810Test |
| حقوق: | all rights reserved ; info:eu-repo/semantics/restrictedAccess |
| رقم الانضمام: | edsbas.37E26BC7 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1137/140999712 |
|---|