We study the asymptotic behavior of the spectrum of the Laplace equation with the Steklov, Dirichlet, Neumann boundary conditions or their combination in a twodimensional domain with small holes of diameter O(ε) as ε → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in ʓ= | ln ε|−1 and power series with rational and holomorphic terms in ʓ respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.

Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition / Chiado' Piat, V.; Nazarov, S. A.. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - 251:5(2020), pp. 655-695. [10.1007/s10958-020-05122-3]

Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition

Chiado' Piat V.;
2020

Abstract

We study the asymptotic behavior of the spectrum of the Laplace equation with the Steklov, Dirichlet, Neumann boundary conditions or their combination in a twodimensional domain with small holes of diameter O(ε) as ε → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in ʓ= | ln ε|−1 and power series with rational and holomorphic terms in ʓ respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.
File in questo prodotto:
File Dimensione Formato  
Piat-Nazarov2020_Article_MixedBoundaryValueProblemsInSi.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 445.19 kB
Formato Adobe PDF
445.19 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Na_2D_2019corr.pdf

embargo fino al 12/11/2021

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 303.81 kB
Formato Adobe PDF
303.81 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2862085