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Title: Inequalities involving heat potentials and Green functions (English)
Author: Watson, Neil A.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 140
Issue: 3
Year: 2015
Pages: 313-318
Summary lang: English
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Category: math
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Summary: We take some well-known inequalities for Green functions relative to Laplace's equation, and prove not only analogues of them relative to the heat equation, but generalizations of those analogues to the heat potentials of nonnegative measures on an arbitrary open set $E$ whose supports are compact polar subsets of $E$. We then use the special case where the measure associated to the potential has point support, in the following situation. Given a nonnegative supertemperature on an open set $E$, we prove a formula for the associated Riesz measure of any point of $E$ in terms of a limit inferior of the quotient of the supertemperature and the Green function for $E$ with a pole at that point. (English)
Keyword: heat potential
Keyword: supertemperature
Keyword: Green function
Keyword: Riesz measure
MSC: 31C05
MSC: 31C15
MSC: 35K05
idZBL: Zbl 06486941
idMR: MR3397259
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Date available: 2015-09-03T10:51:52Z
Last updated: 2018-01-10
Stable URL: http://hdl.handle.net/10338.dmlcz/144397
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Reference: [1] Doob, J. L.: Classical Potential Theory and Its Probabilistic Counterpart.Grundlehren der Mathematischen Wissenschaften 262 Springer, New York (1984). Zbl 0549.31001, MR 0731258
Reference: [2] Watson, N. A.: Introduction to Heat Potential Theory.Mathematical Surveys and Monographs 182 American Mathematical Society, Providence (2012). Zbl 1251.31001, MR 2907452, 10.1090/surv/182
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