Global gradient estimates for P(x)-Laplace equation in non-smooth domains

Chao Zhang; Lihe Wang; Shulin Zhou; Yun Ho Kim

doi:10.3934/cpaa.2014.13.2559

Global gradient estimates for P(x)-Laplace equation in non-smooth domains

Chao Zhang
, Lihe Wang
, Shulin Zhou
, Yun Ho Kim

School of Mathematics

Shanghai Jiao Tong University
University of Iowa
Peking University
Sangmyung University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we consider the global gradient estimates for weak solutions of p(x)-Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, good λ-inequalities, the maximal function technique and the appropriate localization method are the main analytical tools. The global Caldéron- Zygmund theory for such equations is obtained. Moreover, we generalize the regularity estimates in the Lebesgue spaces to the Orlicz spaces.

Original language	English
Pages (from-to)	2559-2587
Number of pages	29
Journal	Communications on Pure and Applied Analysis
Volume	13
Issue number	6
DOIs	https://doi.org/10.3934/cpaa.2014.13.2559
State	Published - Nov 2014

Keywords

BMO space
Elliptic
Gradient estimate
P(x)-Laplacian
Reifenberg domain

Access to Document

10.3934/cpaa.2014.13.2559

Cite this

@article{86deb67063044c86b9718e9d50e59cc5,

title = "Global gradient estimates for P(x)-Laplace equation in non-smooth domains",

abstract = "In this paper we consider the global gradient estimates for weak solutions of p(x)-Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, good λ-inequalities, the maximal function technique and the appropriate localization method are the main analytical tools. The global Cald{\'e}ron- Zygmund theory for such equations is obtained. Moreover, we generalize the regularity estimates in the Lebesgue spaces to the Orlicz spaces.",

keywords = "BMO space, Elliptic, Gradient estimate, P(x)-Laplacian, Reifenberg domain",

author = "Chao Zhang and Lihe Wang and Shulin Zhou and Kim, \{Yun Ho\}",

year = "2014",

month = nov,

doi = "10.3934/cpaa.2014.13.2559",

language = "英语",

volume = "13",

pages = "2559--2587",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "6",

}

TY - JOUR

T1 - Global gradient estimates for P(x)-Laplace equation in non-smooth domains

AU - Zhang, Chao

AU - Wang, Lihe

AU - Zhou, Shulin

AU - Kim, Yun Ho

PY - 2014/11

Y1 - 2014/11

N2 - In this paper we consider the global gradient estimates for weak solutions of p(x)-Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, good λ-inequalities, the maximal function technique and the appropriate localization method are the main analytical tools. The global Caldéron- Zygmund theory for such equations is obtained. Moreover, we generalize the regularity estimates in the Lebesgue spaces to the Orlicz spaces.

AB - In this paper we consider the global gradient estimates for weak solutions of p(x)-Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, good λ-inequalities, the maximal function technique and the appropriate localization method are the main analytical tools. The global Caldéron- Zygmund theory for such equations is obtained. Moreover, we generalize the regularity estimates in the Lebesgue spaces to the Orlicz spaces.

KW - BMO space

KW - Elliptic

KW - Gradient estimate

KW - P(x)-Laplacian

KW - Reifenberg domain

UR - https://www.scopus.com/pages/publications/84904540311

U2 - 10.3934/cpaa.2014.13.2559

DO - 10.3934/cpaa.2014.13.2559

M3 - 文章

AN - SCOPUS:84904540311

SN - 1534-0392

VL - 13

SP - 2559

EP - 2587

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 6

ER -

Global gradient estimates for P(x)-Laplace equation in non-smooth domains

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this