Geodesic
Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: We prove the existence of bounded solutions for the nonlinear elliptic problem $$ -\hbox{\rm div}a(x,u,{\nabla}u)=f \quad\hbox{in }{\Omega}, $$ with $$ a(x,s,\xi)\cdot\xi\geq {\overline M}^{-1}M(h(|s|))M(|\xi|), $$ and $h:{\mathbb{R}^+}{\to }{]0,1]}$ is a continuous monotone decreasing function with unbounded primitive. As regards the $N$-function $M$, no $\Delta_2$-condition is needed.
Classification : 46E30, 35J70, 35J60
Keywords: Orlicz-Sobolev spaces, degenerate coercivity, L-infity-estimates, rearrangements 
@article{EJDE_2007__2007__a290,
     author = {Youssfi, Ahmed},
     title = {Existence of bounded solutions for nonlinear degenerate elliptic equations in {Orlicz} spaces},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a290/}
}
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Youssfi, Ahmed. Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a290/