Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

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, 26 Ciclo. DOI 10.6092/unibo/amsdottorato/6860.
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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.

Tipologia del documento
Tesi di dottorato
Abbondanza, Beatrice
Dottorato di ricerca
Scuola di dottorato
Scienze matematiche, fisiche ed astronomiche
Settore disciplinare
Settore concorsuale
Parole chiave
Potential analysis for second order PDE's with nonnegative characteritic form Subelliptic equations Perron-Wiener and varational solutions Hypoelliptic second order PDEs
Data di discussione
28 Maggio 2015

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