Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2015, Number 3, Pages 35–39 (Mi vmumm237)  
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Continuity of eigenvalues of the Laplace operator according to domain

I. V. Tsylin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: A new proof of the following fact is proposed. The eigenvalues of the Laplace–Dirichlet operator are continious as functions in the corresponding space in domains satisfying uniform cone condition. The author's approach to this problem is based on a topological version of the upper (lower) limit for sequences of sets.
Key words: uniform cone condition, Laplace–Dirichlet operator, Rayleigh quotient.
Received: 17.01.2014
English version:
Moscow University Mathematics Bulletin, 2015, Volume 70, Issue 3, Pages 136–140
DOI: https://doi.org/10.3103/S0027132215030079
Bibliographic databases:
Document Type: Article
UDC: 517.982.25+517.984
Language: Russian
Citation: I. V. Tsylin, “Continuity of eigenvalues of the Laplace operator according to domain”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 3, 35–39; Moscow University Mathematics Bulletin, 70:3 (2015), 136–140
Citation in format AMSBIB
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