Free Boundary Regularity for Almost-Minimizers

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David , Guy; Engelstein , Max; Toro , Tatiana;
  • Publisher: HAL CCSD
  • Subject: Alt-Caffarelli-Friedman functional | Free boundary problems | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | Mathematics - Analysis of PDEs | 35R35

70 pages. Comments welcome; In this paper we study the free boundary regularity for almost-minimizers of the functional \begin{equation*} J(u)=\int_{\mathcal O} |\nabla u(x)|^2 +q^2_+(x)\chi_{\{u>0\}}(x) +q^2_-(x)\chi_{\{u<0\}}(x)\ dx \end{equation*} where $q_\pm \in L^... View more
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