Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 873-886
University Sidi Mohamed Ben Abdellah, Faculty of Sciences
Dhar El Mahraz,
Laboratory LAMA, Department of Mathematics
P.O. Box 1796 Atlas Fez, Morocco; jbennouna 'at' hotmail.com
University Sidi Mohamed Ben Abdellah, Faculty of Sciences Dhar El Mahraz,
Laboratory LAMA, Department of Mathematics
P.O. Box 1796 Atlas Fez, Morocco; hammoumi.mohamed09 'at' gmail.com
University Moulay Ismail, Faculty of Sciences and Technology,
Department of Mathematics
P.O. Box 509-Boutalamine, 52 000 Errachidia, Morocco; and
University Sidi Mohamed Ben Abdellah, Faculty of Sciences Dhar El Mahraz,
Laboratory LAMA, Department of Mathematics
P.O. Box 1796 Atlas Fez, Morocco; ahmed.youssfi 'at' gmail.com
Abstract. We prove an existence result of bounded solutions for some degenerate nonlinear elliptic equations whose prototype is
-div(w(x)/(1+|u|)θ ∇u) = f - div g, in a bounded open Ω ⊂ RN,
in the setting of the weighted Sobolev spaces W01,p(Ω,w). By means of the relative rearrangement, we prove an L∞-estimate which we use to obtain an existence result.
2010 Mathematics Subject Classification: Primary 35J60; 35J70; 46E35.
Key words: Nonlinear elliptic equations, weighted Sobolev spaces, L∞-estimates, rearrangements.
Reference to this article: J. Bennouna, M. Hammoumi and A. Youssfi: On L∞-regularity result for some degenerate nonlinear elliptic equations. Ann. Acad. Sci. Fenn. Math. 39 (2014), 873-886.
doi:10.5186/aasfm.2014.3946
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