caa a22 4500 445843667 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00526-011-0389-8 doi (NATIONALLICENCE)springer-10.1007/s00526-011-0389-8 Full regularity of a free boundary problem with two phases [Elektronische Daten] [Huiqiang Jiang, Christopher Larsen, Luis Silvestre] Let Ω be a bounded domain in $${\mathbb{R}^{n}, n\geq2}$$ . We use $${\mathcal{M}_{\Omega}}$$ to denote the collection of all pairs of (A, u) such that $${A\subset\Omega}$$ is a set of finite perimeter and $${u\in H^{1}\left( \Omega\right)}$$ satisfies$$u\left( x\right) =0\quad\text{a.e.}x\in A.$$We consider the energy functional$$E_{\Omega}\left( A,u\right) =\int\limits_{\Omega}\left\vert\triangledown u\right\vert ^{2}+P_{\Omega}\left( A\right)$$defined on $${\mathcal{M}_{\Omega}}$$ , where P Ω(A) denotes the perimeter of A inside Ω. Let $${\left( A,u\right)\in\mathcal{M}_{\Omega}}$$ be a minimizer with volume constraint. Our main result is that when n≤7, u is locally Lipschitz and the free boundary ∂A is analytic in Ω. Springer-Verlag, 2011 Jiang Huiqiang Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, 15260, Pittsburgh, PA, USA aut Larsen Christopher Department of Mathematical Sciences, Worcester Polytechnic Institute, 01609, Worcester, MA, USA aut Silvestre Luis Department of Mathematics, University of Chicago, 5734 S. University Avenue, 60637, Chicago, IL, USA aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 301-321 0944-2669 42:3-4<301 2011 42 526 https://doi.org/10.1007/s00526-011-0389-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-011-0389-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jiang Huiqiang Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, 15260, Pittsburgh, PA, USA aut NATIONALLICENCE 700 1- Larsen Christopher Department of Mathematical Sciences, Worcester Polytechnic Institute, 01609, Worcester, MA, USA aut NATIONALLICENCE 700 1- Silvestre Luis Department of Mathematics, University of Chicago, 5734 S. University Avenue, 60637, Chicago, IL, USA aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 301-321 0944-2669 42:3-4<301 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer