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July/August 2014 An inverse mean value property for evolution equations
Alessia E. Kogoj, Ermanno Lanconelli, Giulio Tralli
Adv. Differential Equations 19(7/8): 783-804 (July/August 2014).

Abstract

The aim of this work is to extend a result by Suzuki and Watson concerning an inverse property for caloric functions. Our result applies, in particular, to the heat operator on stratified Lie groups and to Kolmogorov-Fokker-Planck-type operators. We show that the open sets characterizing the solutions to the involved equations, in terms of suitable average operators, have to be the level sets of the fundamental solutions of the relevant operators. The technique adopted exploits the structure of the propagation sets, i.e., the sets where the solutions to the involved equations attain their maximum.

Citation

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Alessia E. Kogoj. Ermanno Lanconelli. Giulio Tralli. "An inverse mean value property for evolution equations." Adv. Differential Equations 19 (7/8) 783 - 804, July/August 2014.

Information

Published: July/August 2014
First available in Project Euclid: 6 May 2014

zbMATH: 1297.35014
MathSciNet: MR3252902

Subjects:
Primary: 35B99, 35H10, 35K65

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 7/8 • July/August 2014
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