Some Classes of Partial Differential Operators modelled on Sub-Laplacians
Biagi, Stefano <1988>
Subject
MAT/05 Analisi matematica
Description
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.
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.