Piscitelli, Gianpaolo (2017) Optimization problems for nonlinear eigenvalues. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Optimization problems for nonlinear eigenvalues |
| Autori: | Autore Email Piscitelli, Gianpaolo gianpaolo.piscitelli@unina.it |
| Data: | 5 Ottobre 2017 |
| Numero di pagine: | 101 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Scienze matematiche e informatiche |
| Ciclo di dottorato: | 29 |
| Coordinatore del Corso di dottorato: | nome email de Giovanni, Francesco francesco.degiovanni2@unina.it |
| Tutor: | nome email Ferone, Vincenzo [non definito] |
| Data: | 5 Ottobre 2017 |
| Numero di pagine: | 101 |
| Parole chiave: | Finsler norm; Anisotropic p-Laplacian; Nonlocal problems |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |
| Depositato il: | 17 Ott 2017 14:21 |
| Ultima modifica: | 14 Mar 2018 11:23 |
| URI: | http://www.fedoa.unina.it/id/eprint/11885 |
| DOI: | 10.6093/UNINA/FEDOA/11885 |
Abstract
This thesis is mainly focused on the study of variational problems and the related elliptic partial differential equations, in which the role usually played by the Euclidean norm is taken by a generic Finslerian norm, whose unit ball is a generic centrally symmetric convex body, called Wulff shape. This kind of problems are called anisotropic problem. We study geometric properties of the eigenvalues of the anisotropic p-Laplacian with Dirichlet or Neumann boundary conditions, where F is a suitable norm. In particular, we find sharp upper and lower bounds for these eigenvalues with respect to an open set. Finally we treat problems associated to non-standard Euler-Lagrange equations, that are called "nonlocal" problems. In particular we study problems where the integral term of the unknown function calculated on the entire domain represents the non-locality.
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