Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 30, pp. 1-18.

Title: Degenerate stationary problems with homogeneous
       boundary conditions
 
Authors: Kaouther Ammar (TU Berlin, Institut fur Mathematik, Germany)
         Hicham Redwane (Univ. Hassan 1, Settat, Morocco)

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.