caa a22 4500 44584325X CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00526-010-0367-6 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0367-6 Two-phase semilinear free boundary problem with a degenerate phase [Elektronische Daten] [Norayr Matevosyan, Arshak Petrosyan] We study minimizers of the energy functional $$\int\limits_{D} [|\nabla u|^2+ \lambda(u^+)^p]\,{\rm d}x$$for $${p\in (0,1)}$$ without any sign restriction on the function u. The distinguished feature of the problem is the lack of nondegeneracy in the negative phase. The main result states that in dimension two the free boundaries $${\Gamma^+=\partial\{u>0\}\cap D}$$ and $${\Gamma^-=\partial\{u<0\}\cap D}$$ are C 1,α -regular, provided $${1-\epsilon_0<p<1}$$ . The proof is obtained by a careful iteration of the Harnack inequality to obtain a nontrivial growth estimate in the negative phase, compensating for the apriori unknown nondegeneracy. Springer-Verlag, 2010 Matevosyan Norayr Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, Cambridge, UK aut Petrosyan Arshak Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA aut Calculus of Variations and Partial Differential Equations Springer-Verlag 41/3-4(2011-07-01), 397-411 0944-2669 41:3-4<397 2011 41 526 https://doi.org/10.1007/s00526-010-0367-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0367-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Matevosyan Norayr Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, Cambridge, UK aut NATIONALLICENCE 700 1- Petrosyan Arshak Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 41/3-4(2011-07-01), 397-411 0944-2669 41:3-4<397 2011 41 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer