This paper is aimed at homogenization of an elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives rise to the effect of localization of the eigenfunctions. Moreover, the limit behavior of the lower part of the spectrum can be described in terms of an auxiliary harmonic oscillator operator. We describe the asymptotics of the eigenpairs and derive estimates for the rate of convergence.

Localization effect for a spectral problem in a perforated domain with fourier boundary conditions / CHIADO' PIAT, Valeria; Pankratova, I.; Piatnitski, A.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 45:3(2013), pp. 1302-1327. [10.1137/120868724]

Localization effect for a spectral problem in a perforated domain with fourier boundary conditions

CHIADO' PIAT, Valeria;
2013

Abstract

This paper is aimed at homogenization of an elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives rise to the effect of localization of the eigenfunctions. Moreover, the limit behavior of the lower part of the spectrum can be described in terms of an auxiliary harmonic oscillator operator. We describe the asymptotics of the eigenpairs and derive estimates for the rate of convergence.
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Descrizione: 37 2013 Localization effect
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2624353
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