Advanced Studies in Pure Mathematics

Wiener criterion for Cheeger $p$-harmonic functions on metric spaces

Jana Björn

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Abstract

We show that for Cheeger $p$-harmonic functions on doubling metric measure spaces supporting a Poincaré inequality, the Wiener criterion is necessary and sufficient for regularity of boundary points.

Article information

Source
Potential Theory in Matsue, H. Aikawa, T. Kumagai, Y. Mizuta and N. Suzuki, eds. (Tokyo: Mathematical Society of Japan, 2006), 103-115

Dates
Received: 19 March 2005
Revised: 9 August 2005
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1544999683

Digital Object Identifier
doi:10.2969/aspm/04410103

Mathematical Reviews number (MathSciNet)
MR2277826

Zentralblatt MATH identifier
1120.31003

Subjects
Primary: 31C45: Other generalizations (nonlinear potential theory, etc.)
Secondary: 31C15: Potentials and capacities 35J65: Nonlinear boundary value problems for linear elliptic equations 35J60: Nonlinear elliptic equations

Keywords
boundary regularity capacity Cheeger $p$-harmonic doubling metric measure space Poincaré inequality pointwise estimate Wiener criterion

Citation

Björn, Jana. Wiener criterion for Cheeger $p$-harmonic functions on metric spaces. Potential Theory in Matsue, 103--115, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04410103. https://projecteuclid.org/euclid.aspm/1544999683


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