Computational Methods and Function Theory 7 (2007), No. 1, 127--140
Copyright Heldermann Verlag 2007
Peter Ebenfelt
pebenfel@math.ucsd.edu , Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, U.S.A.
Michael Viscardi
viscardi@fas.harvard.edu , Josan Academy, 5524 Rabbit Ridge Rd., San Diego, CA 92130, U.S.A.
We obtain and prove an explicit formula for the solution of the Dirichlet problem in a simply connected bounded domain in the plane with rational holomorphic data. In particular, the solution can be expressed using only two functions: the boundary data function and a Riemann map of the domain.
Keywords: Dirichlet problem, Riemann map, rational solution.
MSC 2000: 30E25, 35J25.
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