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REGULARITY OF BOUNDARY POINTS IN THE DIRICHLET PROBLEM FOR THE HEAT EQUATION

Part of: Higher-dimensional theory Parabolic equations and systems

Published online by Cambridge University Press:  27 August 2014

NEIL A. WATSON
NEIL A. WATSON*
Affiliation:
School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand email [email protected]
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Abstract

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We show that the null limit hypothesis, in the definition of a barrier, can be relaxed for normal boundary points that satisfy a mild additional condition. We also give a simple necessary and sufficient condition for the regularity of semi-singular boundary points.

Keywords

heat equationregularityDirichlet problembarrierPWB solution

MSC classification

Secondary: 35K05: Heat equation 31B05: Harmonic, subharmonic, superharmonic functions 31B20: Boundary value and inverse problems 31B25: Boundary behavior
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 3 , December 2014 , pp. 476 - 485
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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