Bulletin of the Belgian Mathematical Society - Simon Stevin

Bounded solutions for nonlinear elliptic equations with degenerate coercivity and data in an $L\log L$

A. Benkirane, D. Meskine, and A. Youssfi

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Abstract

In this paper, we prove $L^\infty$-regularity for solutions of some nonlinear elliptic equations with degenerate coercivity whose prototype is $$ \left\{\begin{array}{lll} {\rm-div}({\frac{1}{(1+|u|)^{\theta(p-1)}}}|\nabla u|^{p-2}{\nabla u})=f&{\rm in}&\Omega, \\ u=0&{\rm on}& \partial{\Omega}, \end{array} \right. $$ where $\Omega$ is a bounded open set in ${\rm \mathbb{R}^N}$, $N\geq 2$, $1<p<N$, $\theta$ is a real such that $0\leq\theta\leq1$ and $f\in L^{\frac{N}{p}}log^{\alpha}L$ with some $\alpha>0.$

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 2 (2008), 369-375.

Dates
First available in Project Euclid: 8 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1210254830

Mathematical Reviews number (MathSciNet)
MR2424118

Zentralblatt MATH identifier
1157.35359

Subjects
Primary: 35J70: Degenerate elliptic equations 35J60: Nonlinear elliptic equations 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Zygmund spaces nonlinear elliptic equations $L^{\infty}$-estimates rearrangements

Citation

Benkirane, A.; Youssfi, A.; Meskine, D. Bounded solutions for nonlinear elliptic equations with degenerate coercivity and data in an $L\log L$. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 2, 369--375. https://projecteuclid.org/euclid.bbms/1210254830


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