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Continuity of eigenvalues of the Laplace operator according to domain

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Abstract

A new proof of the following fact is proposed. The eigenvalues of the Laplace-Dirichlet operator are continuous as functions in the corresponding space in domains satisfying the 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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    I. V. Tsylin

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  1. I. V. Tsylin
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Correspondence to I. V. Tsylin.

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Original Russian Text © I.V. Tsylin, 2015, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2015, Vol. 70, No. 3, pp. 35–39.

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Tsylin, I.V. Continuity of eigenvalues of the Laplace operator according to domain. Moscow Univ. Math. Bull. 70, 136–140 (2015). https://doi.org/10.3103/S0027132215030079

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  • DOI: https://doi.org/10.3103/S0027132215030079

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