Inequalities involving heat potentials and Green functions

Watson, Neil A.. "Inequalities involving heat potentials and Green functions." Mathematica Bohemica 140.3 (2015): 313-318. <http://eudml.org/doc/271636>.

@article{Watson2015,
abstract = {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.},
author = {Watson, Neil A.},
journal = {Mathematica Bohemica},
keywords = {heat potential; supertemperature; Green function; Riesz measure},
language = {eng},
number = {3},
pages = {313-318},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inequalities involving heat potentials and Green functions},
url = {http://eudml.org/doc/271636},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Watson, Neil A.
TI - Inequalities involving heat potentials and Green functions
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 3
SP - 313
EP - 318
AB - 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.
LA - eng
KW - heat potential; supertemperature; Green function; Riesz measure
UR - http://eudml.org/doc/271636
ER -