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Malmheden's theorem revisited
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2010 (English)In: Expositiones mathematicae, ISSN 0723-0869, E-ISSN 1878-0792, Vol. 28, no 4, 337-350 p.Article in journal (Refereed) Published
Abstract [en]

In 1934 Malmheden [16] discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin (1957) [8] 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in R-n.

Place, publisher, year, edition, pages
2010. Vol. 28, no 4, 337-350 p.
Keyword [en]
POTENTIAL-THEORY
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-30261DOI: 10.1016/j.exmath.2010.03.002ISI: 000285668100003Scopus ID: 2-s2.0-77958507051OAI: oai:DiVA.org:kth-30261DiVA: diva2:399384
Note
QC 20110222Available from: 2011-02-22 Created: 2011-02-21 Last updated: 2017-12-11Bibliographically approved

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