Acampora, Paolo (2024) Recent advances in geometric problems related to energy efficiency. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Recent advances in geometric problems related to energy efficiency |
| Autori: | Autore Email Acampora, Paolo paolo.acampora@unina.it |
| Data: | 10 Dicembre 2024 |
| 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 gioconda.moscariello@unina.it |
| Tutor: | nome email Trombetti, Cristina [non definito] |
| Data: | 10 Dicembre 2024 |
| Parole chiave: | Shape optimization, free boundary, calculus of variations |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |
| Depositato il: | 29 Ott 2025 09:16 |
| Ultima modifica: | 12 Ago 2026 05:37 |
| URI: | https://www.fedoa.unina.it/id/eprint/16392 |
Abstract
In the present Thesis, we make an attempt to achieve two objectives. The first is to provide a brief overview of classical shape optimization problems and techniques. In particular, we are interested in four categories of problems: existence of an optimum, explicit computation of an optimum, approximation, and stability. The second objective is to present problems that needed to adapt or replace the previously mentioned techniques. In particular, we present: two existence problems related to thermal insulation; three problems in which an explicit minimum (or maximum) can be obtained, those problems are related to p-capacities and spectral inequalities; two first-order development problems by Gamma-convergence of insulation problems with thin layers; finally, we present an optimal stability problem for a special case of Talenti's inequality.
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