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Ratio limit theorem for parabolic horn-shaped domains
Authors:
Pierre Collet, Servet Martinez and Jaime San Martin
Journal:
Trans. Amer. Math. Soc. 358 (2006), 5059-5082
MSC (2000):
Primary 60J65, 60J45, 35K05
Posted:
June 13, 2006
MathSciNet review:
2231885
Full-text PDF Free Access
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Additional Information
Abstract: We prove that for horn-shaped domains of parabolic type, the ratio of the heat kernel at different fixed points has a limit when the time tends to infinity. We also give an explicit formula for the limit in terms of the harmonic functions.
References
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Additional Information
Pierre Collet
Affiliation:
Centre de Physique Théorique, CNRS-UMR 7644 Ecole Polytechnique, 91128 Palaiseau Cedex, France
Email:
Pierre.Collet@cpht.polytechnique.fr
Servet Martinez
Affiliation:
CMM-DIM, UMI 2807-CNRS, Universidad de Chile, Casilla 170-3 Correo 3, Santiago, Chile
Email:
smartine@dim.uchile.cl
Jaime San Martin
Affiliation:
CMM-DIM, UMI 2807-CNRS, Universidad de Chile, Casilla 170-3 Correo 3, Santiago, Chile
Email:
jsanmart@dim.uchile.cl
DOI:
http://dx.doi.org/10.1090/S0002-9947-06-03908-0
PII:
S 0002-9947(06)03908-0
Keywords:
Bessel process,
Harnack inequality,
heat kernel
Received by editor(s):
September 2, 2004
Received by editor(s) in revised form:
November 19, 2004
Posted:
June 13, 2006
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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