Polynomial solutions to Dirichlet problems

Authors:
Marc Chamberland and David Siegel

Journal:
Proc. Amer. Math. Soc. **129** (2001), 211-217

MSC (2000):
Primary 31A25

DOI:
https://doi.org/10.1090/S0002-9939-00-05512-X

Published electronically:
July 27, 2000

MathSciNet review:
1694451

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Abstract | References | Similar Articles | Additional Information

Abstract: The Dirichlet problem

is considered where the functions and are polynomials. The authors study the problem of determining which functions will admit polynomial solutions for any polynomial . When one additionally requires the classical condition , this forces , and a complete classification is obtained. Some necessary conditions are obtained for the case .

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Additional Information

**Marc Chamberland**

Affiliation:
Department of Mathematics and Computer Science, Grinnell College, Grinnell, Iowa 50112-0806

Email:
chamberl@math.grin.edu

**David Siegel**

Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Email:
dsiegel@math.uwaterloo.ca

DOI:
https://doi.org/10.1090/S0002-9939-00-05512-X

Received by editor(s):
February 20, 1998

Received by editor(s) in revised form:
April 5, 1999

Published electronically:
July 27, 2000

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 2000
American Mathematical Society