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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Scaling coupling of reflecting Brownian motions and the hot spots problem


Author: Mihai N. Pascu
Journal: Trans. Amer. Math. Soc. 354 (2002), 4681-4702
MSC (2000): Primary 60J65; Secondary 60J45, 35B05, 35K05
Published electronically: May 7, 2002
MathSciNet review: 1926894
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Abstract: We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.


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Additional Information

Mihai N. Pascu
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Address at time of publication: Department of Mathematics, Purdue Uniwersity, West Lafayette, Indiana 47907-1395
Email: pascu@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03020-9
PII: S 0002-9947(02)03020-9
Keywords: Coupling of diffusions, reflecting Brownian motion, hot spots conjecture, eigenfunctions, Neumann problem, Laplacian
Received by editor(s): September 9, 2001
Received by editor(s) in revised form: January 12, 2002
Published electronically: May 7, 2002
Additional Notes: I would like to thank Richard Bass, Krzysztof Burdzy, Nicolae N. Pascu and Nicolae R. Pascu for several helpful discussions
Article copyright: © Copyright 2002 American Mathematical Society