Gradient estimates for a class of quasilinear elliptic equations with measure data

Fengping Yao; Chao Zhang; Shulin Zhou

doi:10.1007/s11425-017-9205-y

Gradient estimates for a class of quasilinear elliptic equations with measure data

Fengping Yao
, Chao Zhang^*
, Shulin Zhou

^*Corresponding author for this work

School of Mathematics

Shanghai University
Peking University

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

3 Scopus citations

Abstract

We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power.

Original language	English
Pages (from-to)	1719-1730
Number of pages	12
Journal	Science China Mathematics
Volume	62
Issue number	9
DOIs	https://doi.org/10.1007/s11425-017-9205-y
State	Published - 1 Sep 2019

Keywords

35J15
35J92
35R06
Orlicz space
elliptic
measure data
quasilinear
regularity

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10.1007/s11425-017-9205-y

Cite this

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title = "Gradient estimates for a class of quasilinear elliptic equations with measure data",

abstract = "We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power.",

keywords = "35J15, 35J92, 35R06, Orlicz space, elliptic, measure data, quasilinear, regularity",

author = "Fengping Yao and Chao Zhang and Shulin Zhou",

note = "Publisher Copyright: {\textcopyright} 2018, Science China Press and Springer-Verlag GmbH Germany.",

year = "2019",

month = sep,

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doi = "10.1007/s11425-017-9205-y",

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T1 - Gradient estimates for a class of quasilinear elliptic equations with measure data

AU - Yao, Fengping

AU - Zhang, Chao

AU - Zhou, Shulin

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power.

AB - We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power.

KW - 35J15

KW - 35J92

KW - 35R06

KW - Orlicz space

KW - elliptic

KW - measure data

KW - quasilinear

KW - regularity

UR - https://www.scopus.com/pages/publications/85046032277

U2 - 10.1007/s11425-017-9205-y

DO - 10.1007/s11425-017-9205-y

M3 - 文章

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SN - 1674-7283

VL - 62

SP - 1719

EP - 1730

JO - Science China Mathematics

JF - Science China Mathematics

IS - 9

ER -

Gradient estimates for a class of quasilinear elliptic equations with measure data

Abstract

Keywords

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