Piscitelli, Gianpaolo (2017) Optimization problems for nonlinear eigenvalues. [Tesi di dottorato]

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Item Type: Tesi di dottorato
Lingua: English
Title: Optimization problems for nonlinear eigenvalues
Creators:
CreatorsEmail
Piscitelli, Gianpaologianpaolo.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:
nomeemail
de Giovanni, Francescofrancesco.degiovanni2@unina.it
Tutor:
nomeemail
Ferone, VincenzoUNSPECIFIED
Date: 5 October 2017
Number of Pages: 101
Uncontrolled 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

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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