Thermal capacity estimates on the AllenCahn equation
Authors:
Richard B. Sowers and JangMei Wu
Journal:
Trans. Amer. Math. Soc. 351 (1999), 25532567
MSC (1991):
Primary 31B35, 35K57, 60J45
Published electronically:
February 9, 1999
MathSciNet review:
1624210
Fulltext PDF Free Access
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Additional Information
Abstract: We consider the AllenCahn equation in a wellknown scaling regime which gives motion by mean curvature. A wellknown transformation of this PDE, using its standing wave, yields a PDE the solution of which is approximately the distance function to an interface moving by mean curvature. We give bounds on this last fact in terms of thermal capacity. Our techniques hinge upon the analysis of a certain semimartingale associated with a certain PDE (the PDE for the approximate distance function) and an analogue of some results by Bañuelos and Øksendal relating lifetimes of diffusions to exterior capacities.
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Additional Information
Richard B. Sowers
Affiliation:
Department of Mathematics, University of Illinois at UrbanaChampaign, Urbana, Illinois 618012917
Email:
rsowers@math.uiuc.edu
JangMei Wu
Affiliation:
Department of Mathematics, University of Illinois at UrbanaChampaign, Urbana, Illinois 618012917
Email:
wu@math.uiuc.edu
DOI:
http://dx.doi.org/10.1090/S0002994799023995
PII:
S 00029947(99)023995
Keywords:
AllenCahn equation,
mean curvature,
thermal capacity
Received by editor(s):
October 20, 1997
Received by editor(s) in revised form:
April 28, 1998
Published electronically:
February 9, 1999
Additional Notes:
The work of R. S. was supported by NSF Grants DMS 9626398 and DMS 9615877 and the Research Board of the University of Illinois at UrbanaChampaign.
The work of J.M. W. was supported by NSF Grant DMS 9705227.
Article copyright:
© Copyright 1999
American Mathematical Society
