Hölder continuity of ρ(x)-superharmonic functions

A. Lyaghfouri

doi:10.1016/j.na.2010.06.016

Hölder continuity of ρ(x)-superharmonic functions

A. Lyaghfouri

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

13 Citations (Scopus)

Abstract

In this paper we show that a solution of the equation -Δ _ρ(x)u = μ is Hölder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ(Br(x))≤ Crn-^{ρ(x)+α(ρ(x)-1)} for any ball Br(x)⊂ Ω, with r small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpelinen and Zhong for the p-Laplace operator with p constant.

Original language	English
Pages (from-to)	2433-2444
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	73
Issue number	8
DOIs	https://doi.org/10.1016/j.na.2010.06.016
Publication status	Published - Oct 15 2010
Externally published	Yes

Keywords

ρ(x)-Laplace operator
ρ(x)-superharmonic functions
Hölder continuity
Radon measure
Variable exponent Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.na.2010.06.016

Cite this

@article{6b3ee83e51d84c1a95d94bcd05636270,

title = "H{\"o}lder continuity of ρ(x)-superharmonic functions",

abstract = "In this paper we show that a solution of the equation -Δ ρ(x)u = μ is H{\"o}lder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ(Br(x))≤ Crn-ρ(x)+α(ρ(x)-1) for any ball Br(x)⊂ Ω, with r small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpelinen and Zhong for the p-Laplace operator with p constant.",

keywords = "ρ(x)-Laplace operator, ρ(x)-superharmonic functions, H{\"o}lder continuity, Radon measure, Variable exponent Sobolev spaces",

author = "A. Lyaghfouri",

year = "2010",

month = oct,

day = "15",

doi = "10.1016/j.na.2010.06.016",

language = "English",

volume = "73",

pages = "2433--2444",

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

issn = "0362-546X",

publisher = "Elsevier Ltd",

number = "8",

}

TY - JOUR

T1 - Hölder continuity of ρ(x)-superharmonic functions

AU - Lyaghfouri, A.

PY - 2010/10/15

Y1 - 2010/10/15

N2 - In this paper we show that a solution of the equation -Δ ρ(x)u = μ is Hölder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ(Br(x))≤ Crn-ρ(x)+α(ρ(x)-1) for any ball Br(x)⊂ Ω, with r small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpelinen and Zhong for the p-Laplace operator with p constant.

AB - In this paper we show that a solution of the equation -Δ ρ(x)u = μ is Hölder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ(Br(x))≤ Crn-ρ(x)+α(ρ(x)-1) for any ball Br(x)⊂ Ω, with r small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpelinen and Zhong for the p-Laplace operator with p constant.

KW - ρ(x)-Laplace operator

KW - ρ(x)-superharmonic functions

KW - Hölder continuity

KW - Radon measure

KW - Variable exponent Sobolev spaces

UR - https://www.scopus.com/pages/publications/77955467452

UR - https://www.scopus.com/pages/publications/77955467452#tab=citedBy

U2 - 10.1016/j.na.2010.06.016

DO - 10.1016/j.na.2010.06.016

M3 - Article

AN - SCOPUS:77955467452

SN - 0362-546X

VL - 73

SP - 2433

EP - 2444

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 8

ER -

Hölder continuity of ρ(x)-superharmonic functions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this