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Regularity for solutions of nonlinear elliptic equations with degenerate coercivity
Authors:Abdelmoujib Benkirane  Ahmed Youssfi
Affiliation:(1) Department of Mathematics and Informatics, Faculty of Sciences, Dhar El Mahraz University, SidiMohammed Ben Abdallah, PB 1796, Fez-Atlas, Fez, Morocco
Abstract:We prove regularity results for solutions of some nonlinear Dirichlet problems for an equation in the form
$${rm div}left(frac{alphavert nabla uvert^{p-2}nabla u}{(1+vert uvert)^{theta(p-1)}}right) = {rm div}F quad {rm in} Omega,$$
where Ω is a bounded open subset of $${{mathbb{R}}^N}$$ , N  ≥  2, α, θ and p are real constants such that: α  >  0, 0  ≤  θ  ≤  1 and 1  <  p  <  N. A limit case is also considered.
Keywords:Nonlinear elliptic equations  Degenerate coercivity  Regularity  Rearrangements
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