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Localization effect for a spectral problem in a perforated domain with Fourier boundary conditions
Politecnico di Torino, Torino, Italy.
Narvik University College, Narvik, Norway.
Narvik University College, Narvik, Norway; P.N. Lebedev Physical Institute RAS, Moscow, Russian Federation.
2013 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, no 3, p. 1302-1327Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
2013. Vol. 45, no 3, p. 1302-1327
National Category
Mathematics
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URN: urn:nbn:se:hig:diva-27152DOI: 10.1137/120868724OAI: oai:DiVA.org:hig-27152DiVA, id: diva2:1223101
Available from: 2018-06-25 Created: 2018-06-25 Last updated: 2018-06-25Bibliographically approved

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Pankratova, Iryna

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