Piscitelli, Gianpaolo (2017) Optimization problems for nonlinear eigenvalues. [Tesi di dottorato]
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| Item Type: | Tesi di dottorato |
|---|---|
| Resource language: | English |
| Title: | Optimization problems for nonlinear eigenvalues |
| Creators: | Creators Email Piscitelli, Gianpaolo gianpaolo.piscitelli@unina.it |
| Date: | 5 October 2017 |
| Number of Pages: | 101 |
| Institution: | Università degli Studi di Napoli Federico II |
| Department: | 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 UNSPECIFIED |
| Date: | 5 October 2017 |
| Number of Pages: | 101 |
| Keywords: | Finsler norm; Anisotropic p-Laplacian; Nonlocal problems |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |
| Date Deposited: | 17 Oct 2017 14:21 |
| Last Modified: | 14 Mar 2018 11:23 |
| URI: | http://www.fedoa.unina.it/id/eprint/11885 |
| DOI: | 10.6093/UNINA/FEDOA/11885 |
Collection description
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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