Comptes Rendus
Partial Differential Equations
Heat kernels for non-divergence operators of Hörmander type
[Noyaux de la chaleur pour des opérateurs de Hörmander qui ne sont pas sous forme de divergence]
Comptes Rendus. Mathématique, Volume 343 (2006) no. 7, pp. 463-466.

Nous démontrons l'existence d'une solution fondamentale pour une classe d'opérateurs de Hörmander de type chaleur. Pour cette solution fondamentale et ses dérivées nous obtenons des bornes Gaussiennes optimales qui nous permettent de démontrer une inégalité de Harnack invariante.

We prove the existence of a fundamental solution for a class of Hörmander heat-type operators. For this fundamental solution and its derivatives we obtain sharp Gaussian bounds that allow to prove an invariant Harnack inequality.

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DOI : 10.1016/j.crma.2006.09.003

Marco Bramanti 1 ; Luca Brandolini 2 ; Ermanno Lanconelli 3 ; Francesco Uguzzoni 3

1 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
2 Dipartimento di Ingegneria Gestionale e dell'Informazione, Università di Bergamo, Viale Marconi 5, 24044 Dalmine, Italy
3 Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
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     title = {Heat kernels for non-divergence operators of {H\"ormander} type},
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Marco Bramanti; Luca Brandolini; Ermanno Lanconelli; Francesco Uguzzoni. Heat kernels for non-divergence operators of Hörmander type. Comptes Rendus. Mathématique, Volume 343 (2006) no. 7, pp. 463-466. doi : 10.1016/j.crma.2006.09.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.003/

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