Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

Di Marco, Marco (2022) Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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Abstract

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

Abstract
Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Di Marco, Marco
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Generale e applicativo
Ordinamento Cds
DM270
Parole chiave
parabolic p-Laplacian Hormander type vector fields local Lipschitz regularity Moser iteration
Data di discussione della Tesi
22 Luglio 2022
URI

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