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The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces

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 a domain does not have property (KS) provided the boundary contains at least three differrent irreducible algebraic hypersurfaces for which two of them have a common point.

preprint2015arXivOpen access
Hermann Render
math.AP
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Hermann Render

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