A characterization of the Khavinson-Shapiro conjecture via Fischer operators

2015/11/05 by Hermann Render, Render, Hermann
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Nonlinear Partial Differential Equations #math.AP #math.CV #msc:31B05 #msc:35J05

paper · pdf · doi:10.48550/arxiv.1511.01894

6 pages. arXiv admin note: text overlap with arXiv:1511.01747

arxiv created 2015/11/05 · arxiv updated 2015/11/09

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.

Citations

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

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