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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Authors

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

Keywords:

Variational methods, free boundary problems, Linear elliptic equations

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.

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Published

15-12-2021

How to Cite

Samia Challal. (2021). Regularity of the Free Boundary in $div(a(x) \nabla u(x,y) )= -(h(x)\gamma(u))_x$ with $h^\prime (x)<0$. International Journal of Mathematics And Its Applications, 9(4), 1–11. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/23

Issue

Vol. 9 No. 4 (2021)

Section

Research Article

License

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.