Electron. J. Diff. Eqns., Vol. 2008(2008), No. 30, pp. 1-18.

Degenerate stationary problems with homogeneous boundary conditions

Kaouther Ammar, Hicham Redwane

Abstract:
We are interested in the degenerate problem
$$ b(v)-\hbox{ div}a(v,\nabla g(v))=f $$
with the homogeneous boundary condition $g(v)=0$ on some part of the boundary. The vector field $a$ is supposed to satisfy the Leray-Lions conditions and the functions $b,g$ to be continuous, nondecreasing and to verify the normalization condition $b(0)=g(0)=0$ and the range condition $R(b+g)=\mathbb{R}$. Using monotonicity methods, we prove existence and comparison results for renormalized entropy solutions in the $L^1$ setting.

Submitted January 8, 2008. Published February 28. 2008.
Math Subject Classifications: 35K65, 35F30, 35K35, 65M12.
Key Words: Degenerate; homogenous boundary conditions; diffusion; continuous flux.

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Kaouther Ammar
TU Berlin, Institut für Mathematik, MA 6-3
Strasse des 17. Juni 136, 10623 Berlin, Germany
email: ammar@math.tu-berlin.de, Fax:+4931421110, Tel: +4931429306
Hicham Redwane
Faculté des sciences juridiques, Economiques et Sociales
Université Hassan 1
B.P. 784, Settat, Morocco
email: redwane_hicham@yahoo.fr

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