A Gradient Estimate Related Fractional Maximal Operators for a p-Laplace Problem in Morrey Spaces

In the present paper, we deal with the global regularity estimates for the p-Laplace equations with data in divergence form div(|∇u| p−2∇u)=div(|F| p−2 F) in Ω, in Morrey spaces with natural data F ∈ Lp (Ω; ℝ n ) and nonhomogeneous boundary data belongs to W 1,p (Ω). Motivated by the work of [M.-P. Tran, T.-N. Nguyen, New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data, J. Differential Equations 268 (2020), no. 4, 1427–1462], this paper extends that of global Lorentz–Morrey radient estimates in which the ‘good-λ’ technique was undertaken for a class of more general equations, and further, global regularity of weak solutions will be given in terms of fractional maximal operators.