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

2015/11/05 by Hermann Render, Render, Hermann · 1 citation
Mathematics · #31B05 #35J05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:31B05 #msc:35J05

paper · pdf · doi:10.48550/arxiv.1511.01747

10 pages

arxiv created 2015/11/05 · arxiv updated 2015/11/06

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 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.

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