Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form

Di Francesco, Marco ; Polidoro, Sergio (2006) Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form. [Preprint]

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Abstract

We prove some Schauder type estimates and an invariant Harnack inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Di Francesco, Marco
Polidoro, Sergio
Keywords
Parabolic partial differential equations, fundamental solution, Harnack inequality, Schauder estimates
Subjects
Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
DOI
10.6092/unibo/amsacta/2195
Deposit date
21 Aug 2006
Last modified
17 Feb 2016 14:53
URI
https://amsacta.unibo.it/id/eprint/2195

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