{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:55:37Z","timestamp":1777449337653,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T00:00:00Z","timestamp":1462233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2016,5,3]]},"abstract":"<jats:p>In this paper we study the asymptotic behaviour as [Formula: see text] of the spectrum of the elliptic operator [Formula: see text] posed in a bounded domain [Formula: see text] ([Formula: see text]) subject to Dirichlet boundary conditions on [Formula: see text]. When [Formula: see text] both coefficients [Formula: see text] and [Formula: see text] become high contrast in a small neighborhood of a hyperplane \u0393 intersecting \u03a9. We prove that the spectrum of [Formula: see text] converges to the spectrum of an operator acting in [Formula: see text] and generated by the operation [Formula: see text] in [Formula: see text], Dirichlet boundary conditions on [Formula: see text] and certain interface conditions on \u0393 containing the spectral parameter in a nonlinear manner. The eigenvalues of this operator may accumulate at a finite point. Then we study the same problem, when \u03a9 is an infinite straight strip (\u201cwaveguide\u201d) and \u0393 is parallel to its boundary. We show that [Formula: see text] has at least one gap in the spectrum when \u03b5 is small enough and describe the asymptotic behaviour of this gap as [Formula: see text]. The proofs are based on methods of homogenization theory.<\/jats:p>","DOI":"10.3233\/asy-161363","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T16:45:21Z","timestamp":1462293921000},"page":"91-130","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Spectral properties of an elliptic operator with double-contrast coefficients near a hyperplane"],"prefix":"10.1177","volume":"98","author":[{"given":"Andrii","family":"Khrabustovskyi","sequence":"first","affiliation":[{"name":"Institute for Analysis, Department of Mathematics, Karlsruhe Institute of Technology, Englerstra\u00dfe 2, 76131 Karlsruhe, Germany. 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