Continuity of the Laplace operator eigenvalues with respect to domain / I. V. Tsylin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 3. P. 35-39 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 136-140].
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.