Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth

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, R0)-vanishing in x ∈ Ω.

Keywords

• nonlinear elliptic equations
• orlicz growth
• lorentz estimate of the variable power
• log-hölder continuity
• (δ, r0)-vanishing of (a, ω)
• 35j60
• 35b65