Removable sets for hölder continuous p(x)-harmonic functions

A. Lyaghfouri

doi:10.1142/S021953051250008X

Removable sets for hölder continuous p(x)-harmonic functions

A. Lyaghfouri

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

1 Citation (Scopus)

Abstract

We establish that a closed set E is removable for C ^0,α Hölder continuous p(x)-harmonic functions in a bounded open domain Ω of ℝ ⁿ, n ≥ 2, provided that for each compact subset K of E, the (n - pK + α(pK - 1))-Hausdorff measure of K is zero, where p _K = max _x∈K p(x).

Original language	English
Pages (from-to)	199-206
Number of pages	8
Journal	Analysis and Applications
Volume	10
Issue number	2
DOIs	https://doi.org/10.1142/S021953051250008X
Publication status	Published - Apr 2012
Externally published	Yes

Keywords

Hausdorff measure
Hölder continuity
p(x)-harmonic functions
removable sets
variable exponents Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1142/S021953051250008X

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title = "Removable sets for h{\"o}lder continuous p(x)-harmonic functions",

abstract = "We establish that a closed set E is removable for C 0,α H{\"o}lder continuous p(x)-harmonic functions in a bounded open domain Ω of ℝ n, n ≥ 2, provided that for each compact subset K of E, the (n - pK + α(pK - 1))-Hausdorff measure of K is zero, where p K = max x∈K p(x).",

keywords = "Hausdorff measure, H{\"o}lder continuity, p(x)-harmonic functions, removable sets, variable exponents Sobolev spaces",

author = "A. Lyaghfouri",

year = "2012",

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doi = "10.1142/S021953051250008X",

language = "English",

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pages = "199--206",

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T1 - Removable sets for hölder continuous p(x)-harmonic functions

AU - Lyaghfouri, A.

PY - 2012/4

Y1 - 2012/4

N2 - We establish that a closed set E is removable for C 0,α Hölder continuous p(x)-harmonic functions in a bounded open domain Ω of ℝ n, n ≥ 2, provided that for each compact subset K of E, the (n - pK + α(pK - 1))-Hausdorff measure of K is zero, where p K = max x∈K p(x).

AB - We establish that a closed set E is removable for C 0,α Hölder continuous p(x)-harmonic functions in a bounded open domain Ω of ℝ n, n ≥ 2, provided that for each compact subset K of E, the (n - pK + α(pK - 1))-Hausdorff measure of K is zero, where p K = max x∈K p(x).

KW - Hausdorff measure

KW - Hölder continuity

KW - p(x)-harmonic functions

KW - removable sets

KW - variable exponents Sobolev spaces

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U2 - 10.1142/S021953051250008X

DO - 10.1142/S021953051250008X

M3 - Article

AN - SCOPUS:84859134776

SN - 0219-5305

VL - 10

SP - 199

EP - 206

JO - Analysis and Applications

JF - Analysis and Applications

IS - 2

ER -

Removable sets for hölder continuous p(x)-harmonic functions

Abstract

Keywords

ASJC Scopus subject areas

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