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SPECTRUM OF THE LAPLACIAN IN A NARROW CURVED STRIP WITH COMBINED DIRICHLET AND NEUMANN BOUNDARY CONDITIONS
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SYSNO ASEP 0330433 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title SPECTRUM OF THE LAPLACIAN IN A NARROW CURVED STRIP WITH COMBINED DIRICHLET AND NEUMANN BOUNDARY CONDITIONS Author(s) Krejčiřík, David (UJF-V) RID Source Title ESAIM-Control Optimisation and Calculus of Variations. - : EDP Sciences - ISSN 1292-8119
Roč. 15, č. 3 (2009), s. 555-568Number of pages 14 s. Language eng - English Country FR - France Keywords Laplacian in tubes ; Dirichlet and Neumann boundary conditions ; dimension reduction Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000268125200004 DOI 10.1051/cocv:2008035 Annotation We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one is the biggest. We also show that the asymptotics can be obtained from a form of norm-resolvent convergence which takes into account the width-dependence of the domain of definition of the operators involved. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2010
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