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.
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Render, H. A Characterization of the Khavinson-Shapiro Conjecture Via Fischer Operators. Potential Anal 45, 539–543 (2016). https://doi.org/10.1007/s11118-016-9555-0
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DOI: https://doi.org/10.1007/s11118-016-9555-0