Title:

Inequalities involving heat potentials and Green functions (English) 
Author:

Watson, Neil A. 
Language:

English 
Journal:

Mathematica Bohemica 
ISSN:

08627959 (print) 
ISSN:

24647136 (online) 
Volume:

140 
Issue:

3 
Year:

2015 
Pages:

313318 
Summary lang:

English 
. 
Category:

math 
. 
Summary:

We take some wellknown 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 
. 
Date available:

20150903T10:51:52Z 
Last updated:

20180110 
Stable URL:

http://hdl.handle.net/10338.dmlcz/144397 
. 
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 
. 