arXiv:1511.01894 Abstract | arXiv Analytics

arXiv:1511.01894 [math.AP]Abstract References Reviews Resources

A characterization of the Khavinson-Shapiro conjecture via Fischer operators

Published 2015-11-05Version 1

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 $\Omega .$

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

Categories: math.AP, math.CV

Subjects: 31B05, 35J05

Keywords: fischer operator, characterization, khavinson-shapiro conjecture states, dirichlet problem, polynomial data

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