Anisotropic elliptic system with variable exponents and degenerate coercivity with Lm data

Abstract

In a bounded open domain , where , with Lipschitz boundary , we consider the Dirichlet problem for the elliptic system given by here, , , represents a vector-valued function, denotes the partial derivative of u with respect to , and the vector fields and are Carathédory functions. In this paper, we focus on nonlinear degenerate anisotropic elliptic systems with variable growth and data, where m is small. Specifically, we consider the case where the right-hand side term f belongs to with 1<m<N. To analyze this problem, we work with an appropriate functional setting that involves anisotropic Sobolev spaces with variable exponents and weak Lebesgue (Marcinkiewicz) spaces with variable exponents.