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Zeitschrift für Analysis und ihre Anwendungen


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Volume 26, Issue 4, 2007, pp. 459–466
DOI: 10.4171/ZAA/1335

Published online: 2007-12-31

On the Limiting Regularity Result of some Nonlinear Elliptic Equations

M. Kbiri Alaoui[1], D. Meskine[2] and A. Souissi[3]

(1) Ecole Mohammadia d'Ingénieurs, Rabat, Morocco
(2) Ecole Supérieure de Technologie Essaouira, Morocco
(3) Faculté des Sciences, Rabat, Morocco

We shall prove the limiting regularity $W_0^{1,\frac{N(p-1)}{N-1}}(\Omega )$ of solutions of some nonlinear elliptic problems with right hand side in $LLog^{\alpha}L(\Omega)$ and $ \alpha \geq \frac{N - 1}{N}$. Also, an improved regularity is given when $ \alpha < \frac{N - 1}{N}$.

Keywords: Orlicz-Sobolev spaces, truncations, regularity of solutions

Alaoui M. Kbiri, Meskine D., Souissi A.: On the Limiting Regularity Result of some Nonlinear Elliptic Equations. Z. Anal. Anwend. 26 (2007), 459-466. doi: 10.4171/ZAA/1335