Almost minimizers for semilinear free boundary problems with variable coefficients
Olivaine Santana De Queiroz, Leandro S. Tavares · Mathematische Nachrichten · 2018
Abstract We study regularity results for almost minimizers of the functional urn:x-wiley:0025584X:media:mana201600103:mana201600103-math-0001 where is a matrix with Hölder continuous coefficients. In the case we show that an almost minimizer belongs to , where the exponent η is related with the competition between the Hölder continuity of the matrix , the parameter of almost minimization and γ. In some sense, this regularity is optimal. As far as the case is concerned, our results show that an almost minimizer is locally in each phase and , improving in some sense a recent result of David & Toro.