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

Advances in Nonlinear Analysis

article

Shuang Liang¹  Shenzhou Zheng¹ 

[1] Department of Mathematics, Beijing Jiaotong University

关键词: Nonlinear elliptic equations;    Orlicz growth;    Lorentz estimate of the variable power;    log-Hölder continuity;    (δ;    R0)-vanishing of (A;    Ω);   

DOI  :  10.1515/anona-2020-0121

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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 .

【 授权许可】

CC BY