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Homogenization of the spectral problem for periodic elliptic operators with sign-changing density function
Institute for Problems in Mechanical Engineering RAS, St. Petersburgh, Russia.
arvik University College, Narvik, Norway; Ecole Polytechnique CNRS, Palaiseau Cedex, France.
Narvik University College, Narvik, Norway; P. N. Lebedev Physical Institute RAS, Moscow, Russia.
2011 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 200, no 3, p. 747-788Article in journal (Refereed) Published
Abstract [en]

The paper deals with the asymptotic behaviour of spectra of second order self-adjoint elliptic operators with periodic rapidly oscillating coefficients in the case when the density function (the factor on the spectral parameter) changes sign. We study the Dirichlet problem in a regular bounded domain and show that the spectrum of this problem is discrete and consists of two series, one of them tending towards +∞ and another towards −∞. The asymptotic behaviour of positive and negative eigenvalues and their corresponding eigenfunctions depends crucially on whether the average of the weight function is positive, negative or equal to zero. We construct the asymptotics of eigenpairs in all three cases.

Place, publisher, year, edition, pages
2011. Vol. 200, no 3, p. 747-788
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-27155DOI: 10.1007/s00205-010-0370-2OAI: oai:DiVA.org:hig-27155DiVA, id: diva2:1223094
Available from: 2018-06-25 Created: 2018-06-25 Last updated: 2018-06-25Bibliographically approved

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Pankratova, Iryna L.

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