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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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.

Tipologia del documento
Tesi di dottorato
Biagi, Stefano
Dottorato di ricerca
Scuola di dottorato
Scienze matematiche, fisiche ed astronomiche
Settore disciplinare
Settore concorsuale
Parole chiave
left-invariance on real Lie groups, fundamental solution, Strong Maximum Principle
Data di discussione
9 Maggio 2017

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