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Proceedings of the American Mathematical Society

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A symmetry problem from probability

Authors: Stephen J. Fromm and Patrick McDonald
Journal: Proc. Amer. Math. Soc. 125 (1997), 3293-3297
MSC (1991): Primary 35J40, 60J65, 58G32
MathSciNet review: 1425121
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Abstract: We examine solutions of two related boundary value problems for smooth domains in Euclidean space which arise from variational problems in probability. We show that the existence of solutions to each problem implies that the domain is a sphere.

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Additional Information

Stephen J. Fromm
Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071

Patrick McDonald
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Address at time of publication: Department of Mathematics, New College, University of South Florida, Sarasota, Florida 34243

Keywords: Poisson problem, overdetermined boundary value problem
Received by editor(s): June 5, 1996
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1997 American Mathematical Society