Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 54, pp. 1-13.
Title: Existence of bounded solutions for nonlinear degenerate
elliptic equations in Orlicz spaces
Author: Ahmed Youssfi (Univ. Sidi Mohammed Ben Abdallah, Morocco)
Abstract:
We prove the existence of bounded solutions for the
nonlinear elliptic problem
$$
-\mathop{\rm div}a(x,u,{\nabla}u)=f \quad\text{in }{\Omega},
$$
with $u\in W^1_0L_M({\Omega})\cap L^{\infty}(\Omega)$, where
$$
a(x,s,\xi)\cdot\xi\geq {\overline M}^{-1}M(h(|s|))M(|\xi|),
$$
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.
Submitted December 11, 2006. Published April 10, 2007.
Math Subject Classifications: 46E30, 35J70, 35J60.
Key Words: Orlicz-Sobolev spaces; degenerate coercivity;
L-infity-estimates; rearrangements.