PORTO @ 
Archivio Istituzionale della Ricerca
IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili.
EnglishWe consider the problem of maximizing the first eigenvalue of the p-Laplacian (possibly with nonconstant coefficients) over a fixed domain Ω, with Dirichlet conditions along ∂Ω and along a supplementary set Σ, which is the unknown of the optimization problem. The set Σ, which plays the role of a supplementary stiffening rib for a membrane Ω, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in Ω and is subject to the constraint of an upper bound L to its total length (one-dimensional Hausdorff measure). This upper bound prevents Σ from spreading throughout Ω and makes the problem well-posed. We investigate the behavior of optimal sets ΣL as L → ∞ via Γ-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as p→∞ with L fixed, finding connections with maximum-distance problems related to the principal frequency of the ∞-Laplacian.
Asymptotics of the First Laplace Eigenvalue with Dirichlet Regions of Prescribed Length / Tilli P.; Zucco D.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 45:(2013), pp. 3266-3282. [10.1137/130916825]
| Titolo: | Asymptotics of the First Laplace Eigenvalue with Dirichlet Regions of Prescribed Length | |
| Autori: | ||
| Data di pubblicazione: | 2013 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1137/130916825 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| tilli_zucco_published.pdf | 2. Post-print / Author's Accepted Manuscript | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2521687
Copyright © 2022