Degenerate stationary problems with homogeneous boundary conditions

Abstract

We are interested in the degenerate problem $$ b(v)-hbox{ div}a(v, abla g(v))=f $$ 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.

Keywords

• Degenerate
• homogenous boundary conditions
• diffusion
• continuous flux