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On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary

Abstract: We construct two-term asymptotics ?? k = ?m?2(M + ??k + O(?3/2)) of eigenvalues of a mixed boundary-value problem in  ? R2 with many heavy (m > 2) concentrated masses near a straight part  of the boundary ?. ? is a small positive parameter related to size and periodicity of the masses; k ? N. The main term M > 0 is common for all eigenvalues but the correction terms ?k , which are eigenvalues of a limit problem with the spectral Steklov boundary conditions on , exhibit the effect of asymptotic splitting in the eigenvalue sequence enabling the detection of asymptotic forms of eigenfunctions. The justification scheme implies isolating and purifying singularities of eigenfunctions and leads to a new spectral problem in weighed spaces with a "strongly" singular weight.

 Fuente: Revista Matemática Complutense January 2018, Volume 31, Issue 1, pp 1?62

 Editorial: Servicio de Publicaciones, Universidad Complutense

 Fecha de publicación: 01/01/2018

 Nº de páginas: 52

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s13163-017-0243-4

 ISSN: 1139-1138,1988-2807

 Proyecto español: MTM2013-44883-P

 Url de la publicación: https://link.springer.com/article/10.1007%2Fs13163-017-0243-4