A characterization of the Khavinson-Shapiro conjecture via Fischer operators

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 $\Omega$ is equivalent to the surjectivity of a Fischer operator associated to the domain $\Omega .$

arXiv comment6 pages. arXiv admin note: text overlap with arXiv:1511.01747