Geodesic
Degenerate stationary problems with homogeneous boundary conditions
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Ammar, Kaouther and Redwane, Hicham},
     title = {Degenerate stationary problems with homogeneous boundary conditions},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2008},
     year = {2008},
     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/