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  • 1. Agranovsky, M.
    et al.
    Khavinson, D.
    Shapiro, Harold
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Malmheden's theorem revisited2010In: Expositiones mathematicae, ISSN 0723-0869, E-ISSN 1878-0792, Vol. 28, no 4, p. 337-350Article in journal (Refereed)
    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.

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