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

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

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 expo...

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Bibliographic Details
Main Authors: Liang Shuang, Zheng Shenzhou
Format: Article
Language:English
Published: De Gruyter 2020-07-01
Series:Advances in Nonlinear Analysis
Subjects:
nonlinear elliptic equations
orlicz growth
lorentz estimate of the variable power
log-hölder continuity
(δ, r0)-vanishing of (a, ω)
35j60
35b65
Online Access:https://doi.org/10.1515/anona-2020-0121
Description
Summary: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.
ISSN:2191-9496
2191-950X

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