- Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form
- Abbondanza, Beatrice <1986>
Subject
- MAT/05 Analisi matematica
Description
- In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.
Date
- 2015-05-28
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-14996
Abbondanza, Beatrice (2015) Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica