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Scaling coupling of reflecting Brownian motions and the hot spots problem
Author(s):
Mihai
N.
Pascu
Journal:
Trans. Amer. Math. Soc.
354
(2002),
4681-4702.
MSC (2000):
Primary 60J65;
Secondary 60J45, 35B05, 35K05
Posted:
May 7, 2002
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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:
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
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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