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Izvestiya: Mathematics, 2003, Volume 67, Issue 6, Pages 1101–1148
DOI: https://doi.org/10.1070/IM2003v067n06ABEH000459 (Mi im459) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions

D. I. Borisov
English version PDF (467 kB) Citations (23)
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DOI: https://doi.org/10.1070/IM2003v067n06ABEH000459
Abstract: We consider a singularly perturbed spectral boundary-value problem for the Laplace operator in a two-dimensional domain with frequently alternating non-periodic boundary conditions. Under certain very weak restrictions on the alternation structure of the boundary conditions, we obtain the first terms of the asymptotic expansions of the eigenelements of this problem. Under still weaker restrictions, we obtain estimates for the rate of convergence of the eigenvalues.
Received: 12.09.2002
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2003, Volume 67, Issue 6, Pages 23–70
DOI: https://doi.org/10.4213/im459
Bibliographic databases:
UDC: 517.956
MSC: 35P05, 35J05, 35B25, 35J25, 35B27
Language: English
Original paper language: Russian
Citation: D. I. Borisov, “Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions”, Izv. RAN. Ser. Mat., 67:6 (2003), 23–70; Izv. Math., 67:6 (2003), 1101–1148
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v67/i6/p23
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:627
    Russian version PDF:273
    English version PDF:31
    References:96
    First page:2
     
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