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Potential Analysis

, Volume 45, Issue 3, pp 539–543 | Cite as

A Characterization of the Khavinson-Shapiro Conjecture Via Fischer Operators

  • Hermann RenderEmail author
Article
  • 59 Downloads

Abstract

The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet problem for polynomial data is polynomial. In this paper we show that property (KS) for a domain Ω is equivalent to the surjectivity of a Fischer operator associated to the domain Ω.

Keywords

Dirichlet problem Harmonic extension Khavinson-Shapiro conjecture 

Mathematics Subject Classification (2010)

31B05 35J05 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity College DublinBelfieldIreland

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