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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

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.

MSC:

35R35 Free boundary problems for PDEs
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