Volume 26, 2020
|Number of page(s)||47|
|Published online||25 June 2020|
Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications
Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca,
Via Cozzi 55,
2 Dipartimento di Scienza dei Materiali, Università di Milano–Bicocca, Via Cozzi 55, 20125 Milano, Italy.
3 Matematiska institutionen, Stockholms universitet, 106 91 Stockholm, Sweden.
* Corresponding author: firstname.lastname@example.org
Accepted: 7 April 2019
We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.
Mathematics Subject Classification: 35P20 / 35P15 / 35J25
Key words: Mixed boundary conditions / asymptotics of eigenvalues / Aharonov–Bohm eigenvalues
© EDP Sciences, SMAI 2020
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