In this paper we prove existence and regularity of weak solutions for the following system align* cases &u=v=0 \ on \ Ω. cases align* where Ω is an open bounded subset of RN, N>2, f Lᵐ (Ω), where m>1 and g, h are two Carathéodory functions, which may be non monotone. We prove that under appropriate conditions on g and h, there is gain of Sobolev and Lebesgue regularity for the solutions of this system.
Miranda et al. (Wed,) studied this question.
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