Abstract
We consider a class of two-dimensional free boundary problems of type $div(a(X) \nabla u) = -div(\chi (u)H(X))$, where $H$ is a Lipschitz vector function satisfying $div(H(X))\geq 0$. We prove that the free boundary $\partial [u>0] \cap\Omega$ is represented locally by a family of continuous functions.
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