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On the classical Dirichlet problem in the plane with rational data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2006 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 100, 157-190 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2006. Vol. 100, 157-190 p.
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URN: urn:nbn:se:kth:diva-37349DOI: 10.1007/BF02916759ISI: 000245687800006ScopusID: 2-s2.0-34247464655OAI: diva2:433366
Available from: 2011-08-09 Created: 2011-08-09 Last updated: 2011-08-09Bibliographically approved

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Shapiro, Harold S.
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