Local behavior of p-harmonic Green's functions in metric spaces

Donatella Danielli; Nicola Garofalo; Niko Marola

doi:10.1007/s11118-009-9154-4

Local behavior of p-harmonic Green's functions in metric spaces

Donatella Danielli, Nicola Garofalo, Niko Marola

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

13 Scopus citations

Abstract

We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality.

Original language	English (US)
Pages (from-to)	343-362
Number of pages	20
Journal	Potential Analysis
Volume	32
Issue number	4
DOIs	https://doi.org/10.1007/s11118-009-9154-4
State	Published - May 2010
Externally published	Yes

Keywords

Capacity
Doubling measure
Green function
Metric space
Minimizer
Newtonian space
Singular function
Sobolev space
p-Dirichlet integral
p-Laplace equation and Poincaré inequality
p-harmonic

ASJC Scopus subject areas

Analysis

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10.1007/s11118-009-9154-4

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title = "Local behavior of p-harmonic Green's functions in metric spaces",

abstract = "We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincar{\'e} inequality.",

keywords = "Capacity, Doubling measure, Green function, Metric space, Minimizer, Newtonian space, Singular function, Sobolev space, p-Dirichlet integral, p-Laplace equation and Poincar{\'e} inequality, p-harmonic",

author = "Donatella Danielli and Nicola Garofalo and Niko Marola",

note = "Funding Information: First author supported in part by NSF CAREER Grant, DMS-0239771. Second author supported in part by NSF Grant DMS-0701001. Third author supported by the Academy of Finland and the Emil Aaltonen foundation.",

year = "2010",

month = may,

doi = "10.1007/s11118-009-9154-4",

language = "English (US)",

volume = "32",

pages = "343--362",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

number = "4",

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TY - JOUR

T1 - Local behavior of p-harmonic Green's functions in metric spaces

AU - Danielli, Donatella

AU - Garofalo, Nicola

AU - Marola, Niko

N1 - Funding Information: First author supported in part by NSF CAREER Grant, DMS-0239771. Second author supported in part by NSF Grant DMS-0701001. Third author supported by the Academy of Finland and the Emil Aaltonen foundation.

PY - 2010/5

Y1 - 2010/5

N2 - We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality.

AB - We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality.

KW - Capacity

KW - Doubling measure

KW - Green function

KW - Metric space

KW - Minimizer

KW - Newtonian space

KW - Singular function

KW - Sobolev space

KW - p-Dirichlet integral

KW - p-Laplace equation and Poincaré inequality

KW - p-harmonic

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UR - http://www.scopus.com/inward/citedby.url?scp=77950458676&partnerID=8YFLogxK

U2 - 10.1007/s11118-009-9154-4

DO - 10.1007/s11118-009-9154-4

M3 - Article

AN - SCOPUS:77950458676

SN - 0926-2601

VL - 32

SP - 343

EP - 362

JO - Potential Analysis

JF - Potential Analysis

IS - 4

ER -

Local behavior of p-harmonic Green's functions in metric spaces

Abstract

Keywords

ASJC Scopus subject areas

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