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On the classical Dirichlet problem in the plane with rational data |
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| Authors: | S R Bell P Ebenfelt D Khavinson H S Shapiro |
| Institution: | (1) Department of Mathematics, Purdue University, 47907 West Lafayette, IN, USA;(2) Department of Mathematics, University of California, San Diego, 92093-0112 La Jolla, CA, USA;(3) Department of Mathematics, University of Arkansas, 72701 Fayetteville, AR, USA;(4) Present address: Department of Mathematics, University of South Florida, 33620-5700 Tampa, FL, USA;(5) Department of Mathematics, Royal Instttute of Technology, S-100 44 Stockholm, Sweden |
| Abstract: | We consider the Dirichlet problem for the Laplace operator with rational data on the boundary of a planar domain. Our main results include a characterization of the disk as the only domain for which all solutions are rational and a characterization of the simply connected quadrature domains as the only ones for which all solutions are algebraic of a certain type. The first three authors were partially supported by the NSF grants DMS-0305958, DMS-0401215 and DMS-0139008 respectively. |
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