Abstract
In this paper, we are going to study the following elliptic system: [Formula: see text] where Ω is a bounded open subset of ℝN, a(x, s) and b(x, s) are positive and coercive Carathéodory functions, and f ∈ LM(Ω). The main purpose of this paper is to prove existence and regularity results with an improved regularity of the function z in the class of Sobolev spaces, and the existence of solutions (u, z) both with finite energy.
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