Advances in Differential Equations

Uniform Gaussian estimates for the fundamental solutions for heat operators on Carnot groups

A. Bonfiglioli, E. Lanconelli, and F. Uguzzoni

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Abstract

In this paper, we are concerned with existence, qualitative properties, and uniform Gaussian estimates of the global fundamental solutions of a family of heat operators on Carnot groups. As a byproduct, we obtain existence and uniqueness theorems of Thychonov type for the Cauchy problem. Our effort here is also to provide simple and direct proofs relying on few basic tools such as invariant Harnack inequalities and maximum principles. In our study, we thoroughly exploit some structural properties of Carnot groups pointed out in the previous paper [4].

Article information

Source
Adv. Differential Equations Volume 7, Number 10 (2002), 1153-1192.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651633

Mathematical Reviews number (MathSciNet)
MR1919700

Zentralblatt MATH identifier
1036.35061

Subjects
Primary: 35H20: Subelliptic equations
Secondary: 35A08: Fundamental solutions 43A80: Analysis on other specific Lie groups [See also 22Exx]

Citation

Bonfiglioli, A.; Lanconelli, E.; Uguzzoni, F. Uniform Gaussian estimates for the fundamental solutions for heat operators on Carnot groups. Adv. Differential Equations 7 (2002), no. 10, 1153--1192. https://projecteuclid.org/euclid.ade/1356651633.


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