Abstract
Abstract In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, while the nonlinearity and underlying domain (A, Ω) is (δ, R 0)-vanishing in x ∈ Ω.
Highlights
Throughout this paper, let Ω ⊂ Rn for n ≥ be a given bounded domain with its rough boundary speci ed later
In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth
It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, while the nonlinearity and underlying domain (A, Ω) is (δ, R )-vanishing in x ∈ Ω
Summary
Throughout this paper, let Ω ⊂ Rn for n ≥ be a given bounded domain with its rough boundary speci ed later. Given a vectorial valued function f = (f , f , · · · , f n) : Ω → Rn. Given a vectorial valued function f = (f , f , · · · , f n) : Ω → Rn The aim of this present article is to study a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients of weak solutions to the zero-Dirichlet problem of general nonlinear elliptic equations div A(x, Du) =div G(x, f ) in Ω,.
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