Continuity of eigenvalues of the Laplace operator according to domain
I. V. Tsylin · Moscow University Mathematics Bulletin · 2015
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.