Challal, S.; Lyaghfouri, A. On a class of free boundary problems of type \( \text{div}(a(X)\nabla u)=-\text{div}(\chi (u)H(X))\). (English) Zbl 1212.35508 Differ. Integral Equ. 19, No. 5, 481-516 (2006). Summary: We consider a class of two-dimensional free boundary problems of type \(\text{div}(a(X)\nabla u)=-\text{div}(\chi (u)H(X))\), where \(H\) is a Lipschitz vector function satisfying \(\text{div}(H(X))\geq 0\). We prove that the free boundary \(\partial [u>0]\cap \Omega \) is represented locally by a family of continuous functions. Cited in 6 Documents MSC: 35R35 Free boundary problems for PDEs Keywords:two-dimensional free boundary problem; Lipschitz-continuous vector function PDFBibTeX XMLCite \textit{S. Challal} and \textit{A. Lyaghfouri}, Differ. Integral Equ. 19, No. 5, 481--516 (2006; Zbl 1212.35508)