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- W3151428766 abstract "Let $Omegasubsetmathbb{C}$ be a bounded domain such that there exists an algebraic harmonic function of degree two vanishing on the boundary of $Omega.$ Then we show that the Khavinson-Shapiro conjecture holds for $Omega:$ if the Dirichlet problem on $Omega$ with all polynomial boundary data have polynomial solutions, then $Omega$ must be an ellipse. We also prove that if there exists a rational function with a singularity in $Omega$, such that the Dirichlet problem for its restriction on $partialOmega$ along with all polynomial functions have rational solutions, then $Omega$ must be a disc. This generalizes a well-known result by Bell, Ebenfelt, Khavinson, and Shapiro. Our proofs are purely algebraic." @default.
- W3151428766 created "2021-04-13" @default.
- W3151428766 creator A5071143950 @default.
- W3151428766 date "2021-04-05" @default.
- W3151428766 modified "2023-09-27" @default.
- W3151428766 title "On the Dirichlet problem in the plane with polynomial data" @default.
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