Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications

¹ Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, Via Cozzi 55, 20125 Milano, Italy.
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: veronica.felli@unimib.it

Received: 27 April 2018
Accepted: 7 April 2019

Abstract

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.