Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces

• Main Author: Ahmed Youssfi
• Format: Article
• Language: English
• Published: Texas State University 2007-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Orlicz-Sobolev spaces; degenerate coercivity; L-infity-estimates; rearrangements.
• Online Access: http://ejde.math.txstate.edu/Volumes/2007/54/abstr.html

We prove the existence of bounded solutions for the nonlinear elliptic problem$$ -mathop{m div}a(x,u,{ abla}u)=f quadext{in }{Omega},$$ with $uin W^1_0L_M({Omega})cap L^{infty}(Omega)$, where$$ a(x,s,xi)cdotxigeq {overline M}^{-1}M(h(|s|))M(|xi|),$$ and $h:{mathbb{R}^+}{o }{]0,1]}$ is a continuous monotone decreasing function with unbounded primitive. As regards the $N$-function $M$, no $Delta_2$-condition is needed.