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CALORIC MEASURE FOR ARBITRARY OPEN SETS

Published online by Cambridge University Press:  04 March 2013

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

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We give a systematic treatment of caloric measure for arbitrary open sets. The caloric measure is defined only on the essential boundary of the set. Our main result gives criteria for the resolutivity of essential boundary functions, and their integral representation in terms of caloric measure. We also characterize the caloric measure null sets in terms of the boundary singularities of nonnegative supertemperatures.

Keywords

hypotemperaturehypertemperaturecaloric measureDirichlet problem
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 3 , June 2012 , pp. 391 - 407
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

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