Advances in Differential Equations

An inverse mean value property for evolution equations

Alessia E. Kogoj, Ermanno Lanconelli, and Giulio Tralli

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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.

Article information

Source
Adv. Differential Equations Volume 19, Number 7/8 (2014), 783-804.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1399395726

Mathematical Reviews number (MathSciNet)
MR3252902

Zentralblatt MATH identifier
1297.35014

Subjects
Primary: 35K65: Degenerate parabolic equations 35H10: Hypoelliptic equations 35B99: None of the above, but in this section

Citation

Kogoj, Alessia E.; Lanconelli, Ermanno; Tralli, Giulio. An inverse mean value property for evolution equations. Adv. Differential Equations 19 (2014), no. 7/8, 783--804. https://projecteuclid.org/euclid.ade/1399395726.


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