Geodesic
Degenerate stationary problems with homogeneous boundary conditions
Electronic journal of differential equations, Tome 2008 (2008)
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.
Classification : 35K65, 35F30, 35K35, 65M12
Keywords: degenerate, homogenous boundary conditions, diffusion, continuous flux 
@article{EJDE_2008__2008__a71,
     author = {Ammar,  Kaouther and Redwane,  Hicham},
     title = {Degenerate stationary problems with homogeneous boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1138.35352},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a71/}
}
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Ammar,  Kaouther; Redwane,  Hicham. Degenerate stationary problems with homogeneous boundary conditions. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a71/