Global regularity estimates for a class of quasilinear elliptic equations in the whole space

Fengping Yao; Chao Zhang; Shulin Zhou

doi:10.1016/j.na.2018.07.004

Global regularity estimates for a class of quasilinear elliptic equations in the whole space

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

2 Scopus citations

Abstract

In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f∈BMO(Rⁿ)⇒∇u∈BMO(Rⁿ)for the weak solutions of a class of quasilinear elliptic equations diva∇u∇u=divfinRⁿ,where B(t)=∫₀ ^tτa(τ)dτ for t≥0. Meanwhile, we use the iteration-covering procedure to prove that Bf∈L^q(Rⁿ)⇒B∇u∈L^q(Rⁿ)for anyq>1for the weak solutions of diva∇u∇u=divaffinRⁿ.Moreover, we remark that a(t)=t^p−2(p-Laplace equation)anda(t)=t^p−2log(1+t)satisfy the given conditions in this work.

Original language	English
Article number	111307
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	194
DOIs	https://doi.org/10.1016/j.na.2018.07.004
State	Published - May 2020

Keywords

BMO estimates
Divergence
Elliptic
Gradient
L
Quasilinear
Regularity
p-Laplace

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10.1016/j.na.2018.07.004

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title = "Global regularity estimates for a class of quasilinear elliptic equations in the whole space",

abstract = "In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f∈BMO(Rn)⇒∇u∈BMO(Rn)for the weak solutions of a class of quasilinear elliptic equations diva∇u∇u=divfinRn,where B(t)=∫0 tτa(τ)dτ for t≥0. Meanwhile, we use the iteration-covering procedure to prove that Bf∈Lq(Rn)⇒B∇u∈Lq(Rn)for anyq>1for the weak solutions of diva∇u∇u=divaffinRn.Moreover, we remark that a(t)=tp−2(p-Laplace equation)anda(t)=tp−2log(1+t)satisfy the given conditions in this work.",

keywords = "BMO estimates, Divergence, Elliptic, Gradient, L, Quasilinear, Regularity, p-Laplace",

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

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2020",

month = may,

doi = "10.1016/j.na.2018.07.004",

language = "英语",

volume = "194",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - Global regularity estimates for a class of quasilinear elliptic equations in the whole space

AU - Yao, Fengping

AU - Zhang, Chao

AU - Zhou, Shulin

PY - 2020/5

Y1 - 2020/5

N2 - In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f∈BMO(Rn)⇒∇u∈BMO(Rn)for the weak solutions of a class of quasilinear elliptic equations diva∇u∇u=divfinRn,where B(t)=∫0 tτa(τ)dτ for t≥0. Meanwhile, we use the iteration-covering procedure to prove that Bf∈Lq(Rn)⇒B∇u∈Lq(Rn)for anyq>1for the weak solutions of diva∇u∇u=divaffinRn.Moreover, we remark that a(t)=tp−2(p-Laplace equation)anda(t)=tp−2log(1+t)satisfy the given conditions in this work.

AB - In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f∈BMO(Rn)⇒∇u∈BMO(Rn)for the weak solutions of a class of quasilinear elliptic equations diva∇u∇u=divfinRn,where B(t)=∫0 tτa(τ)dτ for t≥0. Meanwhile, we use the iteration-covering procedure to prove that Bf∈Lq(Rn)⇒B∇u∈Lq(Rn)for anyq>1for the weak solutions of diva∇u∇u=divaffinRn.Moreover, we remark that a(t)=tp−2(p-Laplace equation)anda(t)=tp−2log(1+t)satisfy the given conditions in this work.

KW - BMO estimates

KW - Divergence

KW - Elliptic

KW - Gradient

KW - L

KW - Quasilinear

KW - Regularity

KW - p-Laplace

UR - https://www.scopus.com/pages/publications/85050237734

U2 - 10.1016/j.na.2018.07.004

DO - 10.1016/j.na.2018.07.004

M3 - 文章

AN - SCOPUS:85050237734

SN - 0362-546X

VL - 194

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 111307

ER -

Global regularity estimates for a class of quasilinear elliptic equations in the whole space

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Keywords

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