Pascale, Giulio (2024) Variational results on capillary isoperimetric problems and liquid drop models. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Variational results on capillary isoperimetric problems and liquid drop models |
| Autori: | Autore Email Pascale, Giulio giuliopascale95@gmail.com |
| Data: | 7 Dicembre 2024 |
| Numero di pagine: | 150 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 37 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda gmoscari@unina.it |
| Tutor: | nome email Moscariello, Gioconda [non definito] |
| Data: | 7 Dicembre 2024 |
| Numero di pagine: | 150 |
| Parole chiave: | Isoperimetry - Capillarity - Regularity |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |
| Informazioni aggiuntive: | Il sottoscritto afferisce al 37° ciclo di dottorato, assente nel menù a tendina. |
| Depositato il: | 29 Ott 2025 09:15 |
| Ultima modifica: | 12 Ago 2026 05:37 |
| URI: | https://www.fedoa.unina.it/id/eprint/16346 |
Abstract
The main topic of this thesis concerns some recent developments in Calculus of Variations and Geometric Measure Theory. After the introductory Chapter 1, where we present the main results, motivations and history on the topics considered in this thesis, in Chapter 2 we collect the preliminaries needed for the presentation. Chapter 3 is dedicated to the proof of some quantitative isoperimetric inequalities for the classical capillarity problem in a Euclidean halfspace. The results have been obtained in a joint work with M. Pozzetta and are based on a novel combination of a quantitative ABP method with a selection-type method, after a symmetrization procedure. In Chapter 4 we establish some existence and nonexistence results for the volume-constrained minimization problem of an energy functional given by the sum of a capillarity perimeter, a nonlocal interaction term and a gravitational type energy. The strategy stems from an application of the quantitative isoperimetric inequalities for the capillarity problem in a half-space. Chapter 5 is devoted to study differentiability and integrability properties of weak solutions to some nonlinear elliptic systems with growth coefficients in BMO. The results have been obtained in collaboration with G. Moscariello. Moreover we derive some local Calderón–Zygmund estimates, which are relevant to provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals.
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