Regularity of the Free Boundary in $div(a(x) \nabla u(x,y) )= -(h(x)\gamma(u))_x$ with $h^\prime (x)<0$
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Keywords:Variational methods, free boundary problems, Linear elliptic equations
A free boundary problem of type $div(a(x) \nabla u )=-(h(x)\gamma(u))_x$ with $h_x < 0$ is considered. A regularity of the free boundary as a curve $y=\Phi(x)$ is established using a local monotony $b u_x-u_y <0$ close to free boundary points.
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