Malmheden's theorem revisited
2010 (English)In: Expositiones mathematicae, ISSN 0723-0869, Vol. 28, no 4, 337-350 p.Article in journal (Refereed) Published
In 1934 Malmheden  discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin (1957)  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.
IdentifiersURN: urn:nbn:se:kth:diva-30261DOI: 10.1016/j.exmath.2010.03.002ISI: 000285668100003ScopusID: 2-s2.0-77958507051OAI: oai:DiVA.org:kth-30261DiVA: diva2:399384
QC 201102222011-02-222011-02-212011-02-22Bibliographically approved