Regularity of the Free Boundary in $div(a(x) \nabla u(x,y) )= -(h(x)\gamma(u))_x$ with $h^\prime (x)<0$

# Samia Challal1

1Department of Mathematics, Glendon college - York university, 2275 Bayview Ave. Toronto ON M4N 3M6 Canada.

Abstract: 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.
Keywords: Variational methods, free boundary problems, Linear elliptic equations.

Cite this article as: Samia Challal, Two Phases of the Hess Algebraic Decomposition Method Utilized for Watermarking System, Int. J. Math. And Appl., vol. 9, no. 4, 2021, pp. 1-11.

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