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A symmetry problem from probability

Author(s): Stephen J. Fromm; Patrick McDonald
Journal: Proc. Amer. Math. Soc. 125 (1997), 3293-3297.
MSC (1991): Primary 35J40, 60J65, 58G32
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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.

References:

[B]
A. Bennett, Symmetry in an overdetermined fourth order elliptic boundary value problem, SIAM J. Math. Anal. 17 (1986), 1354-1358. MR 87i:35059

[KM1]
K. K. J. Kinateder and P. McDonald, Brownian functionals on hypersurfaces in Euclidean space, Proc. Amer. Math. Soc. 125 (1997), 1815-1822. CMP 97:07

[KM2]
K. K. J. Kinateder and P. McDonald, Hypersurfaces in $\mathbf R^{d}$ and the variance of exit times for Brownian motion, Proc. Amer. Math. Soc. (to appear). CMP 96:16

[S]
J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304-318. MR 48:11545

[W]
H. F. Weinberger, Remark on the preceding paper of Serrin, Arch. Rational Mech. Anal. 43 (1971), 319-320. MR 48:11546

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Additional Information:

Stephen J. Fromm
Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071
Email: fromm@uwyo.edu

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
Email: pmacdona@virtu.sar.usf.edu

DOI: 10.1090/S0002-9939-97-04162-2
PII: S 0002-9939(97)04162-2
Keywords: Poisson problem, overdetermined boundary value problem
Received by editor(s): June 5, 1996
Communicated by: Jeffrey Rauch
Copyright of article: Copyright 1997, American Mathematical Society

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