Parametrix technique for a class of degenerate parabolic operators with measurable coefficients under the weak Hörmander condition

Lucertini, Giacomo (2021) Parametrix technique for a class of degenerate parabolic operators with measurable coefficients under the weak Hörmander condition. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270], Documento full-text non disponibile
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Abstract

In this thesis we study a wide class of differential operators of Kolmogorov type characterized by two structural hypotheses: it is satisfied the weak Hörmander condition and the coefficients are merely measurable in time variable. The main purpose of this work is to adapt the classical Levi parametrix method to this framework, in order to construct a fundamental solution of the operator. In particular, we will use a time-dependent parametrix. This problem is strongly related to the study of stochastic differential equations (SDEs), since the backward Kolmogorov operators associated to some linear SDEs take the form of the operator in the class we have considered. Therefore, the obtained fundamental solution can be seen as the transition density of the solution of a SDE. Choosing coefficients that are merely measurable in time, these results may be applied in the study of stochastic partial differential equations (SPDEs), which naturally appear in applications with rough coefficients.

Abstract
Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Lucertini, Giacomo
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Generale e applicativo
Ordinamento Cds
DM270
Parole chiave
partial differetial equations,Hörmander condition,parametrix,stochastic differential equations,measurable coefficients
Data di discussione della Tesi
29 Ottobre 2021
URI

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