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Decay of a p-harmonic measure in the plane
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, 351-366 p.Article in journal (Refereed) Published
Abstract [en]

We study the asymptotic behaviour of a p-harmonic measure w(p), p is an element of (1, infinity], in a domain Omega subset of R-2, subject to certain regularity constraints. Our main result is that w(p) (B (w, delta) boolean AND partial derivative Omega, w(0)) approximate to delta(q) as delta -> 0(+), where q = q(v,p) is given explicitly as a function of v and p. Here, v is related to properties of Omega near w. If p = infinity, this extends to some domains in R-n. By a result due to Hirata, our result implies that the p-Green function for p is an element of (1, 2) is not quasi-symmetric in plane C-1,C-1-domains.

Place, publisher, year, edition, pages
Suomalainen Tiedeakatemia , 2013. Vol. 38, no 1, 351-366 p.
Keyword [en]
harmonic measure, harmonic function, p-Laplace operator, generalized interior ball
National Category
Mathematics Mathematical Analysis
Research subject
Mathematics; Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-47922DOI: 10.5186/aasfm.2013.3808ISI: 000316239200019OAI: oai:DiVA.org:umu-47922DiVA: diva2:445350
Note

Originally published in thesis in manuscript form

Available from: 2011-10-03 Created: 2011-10-03 Last updated: 2017-12-08Bibliographically approved
In thesis
1. p-harmonic functions near the boundary
Open this publication in new window or tab >>p-harmonic functions near the boundary
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för matematik och matematisk statistik, 2011. 228 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 50
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-47942 (URN)978-91-7459-287-0 (ISBN)
Public defence
2011-10-28, Mit-huset, MA121, Umeå universitet, Umeå, 10:00
Opponent
Supervisors
Available from: 2011-10-07 Created: 2011-10-04 Last updated: 2011-10-04Bibliographically approved

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Lundström, Niklas L.P.

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