Some Classes of Partial Differential Operators modelled on Sub-Laplacians

Biagi, Stefano (2017) Some Classes of Partial Differential Operators modelled on Sub-Laplacians, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica, 28 Ciclo. DOI 10.6092/unibo/amsdottorato/7922.
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Abstract

This thesis concerns with the Theory of Hormander operators and with some classes of hypoelliptic differential operators with non-negative characteristic form. The following are the main problems faced in the thesis. (1) Given a Hormander operator L on the whole of RN, is it possible to find a real Lie group on which L is left-invariant? (2) Given a homogeneous Hormander operator L on RN, there exists a ``well-behaved'' global fundamental solution for L? (3) Given a hypoelliptic partial differential operator L on RN with non-negative characteristic form (not necessarily of Hormander-type), is it possible to prove a Strong Maximum Principle and to develop a satisfactory Potential Theory? Problems (1)-to-(3) are faced with a unitary approach which crucially relies on the study of the geometry of the integral curves of suitable vector fields associated with the operator L and of their composition.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Biagi, Stefano
Supervisore
Dottorato di ricerca
Scuola di dottorato
Scienze matematiche, fisiche ed astronomiche
Ciclo
28
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
left-invariance on real Lie groups, fundamental solution, Strong Maximum Principle
URN:NBN
DOI
10.6092/unibo/amsdottorato/7922
Data di discussione
9 Maggio 2017
URI

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