In this paper we prove the existence of distributional solutions to certain
anisotropic nonlinear weighted elliptic equations with variable exponents, where the weight function belongs to the
anisotropic Sobolev space with variable exponents and zero boundary. The functional setting involves
anisotropic variable exponents Lebesgue–Sobolev spaces.
The aim of this paper is to study the existence and maximal regularity for distributional solutions of degenerate anisotropic nonlinear elliptic systems with variable exponents where the right-hand side f is in L q(•) , q(•) : Ω → (1, +∞). The functional setting involves anisotropic Sobolev spaces with variable exponents as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents.
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