Advanced Studies in Pure Mathematics

On the behavior at infinity for non-negative superharmonic functions in a cone

Minoru Yanagishita

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Abstract

This paper shows that a positive superharmonic function on a cone behaves regularly outside an $\alpha$-minimally thin set in a cone. This fact is known for a half space which is a special cone.

Article information

Source
Potential Theory in Matsue, H. Aikawa, T. Kumagai, Y. Mizuta and N. Suzuki, eds. (Tokyo: Mathematical Society of Japan, 2006), 403-413

Dates
Received: 30 May 2005
Revised: 1 December 2005
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1544999707

Digital Object Identifier
doi:10.2969/aspm/04410403

Mathematical Reviews number (MathSciNet)
MR2279772

Zentralblatt MATH identifier
1116.31002

Subjects
Primary: 31B05: Harmonic, subharmonic, superharmonic functions
Secondary: 31B20: Boundary value and inverse problems

Keywords
cone superharmonic functions $\alpha$-minimally thin sets

Citation

Yanagishita, Minoru. On the behavior at infinity for non-negative superharmonic functions in a cone. Potential Theory in Matsue, 403--413, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04410403. https://projecteuclid.org/euclid.aspm/1544999707


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