4 papers · 1 filter
Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems
Alexandre Girouard, Mikhail Karpukhin, Jean Lagacé
We associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and ot…
Spectral invariants of Dirichlet-to-Neumann operators on surfaces
Jean Lagacé, Simon St-Amant
We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schrödinger operators on compact Riemannian surfaces with boundary. F…
Optimal unions of scaled copies of domains and Pólya's conjecture
Pedro Freitas, Jean Lagacé, Jordan Payette
Given a bounded Euclidean domain , we consider the sequence of optimisers of the Laplacian eigenvalue within the family consisting of all possible disjoint unions o…
Eigenvalue optimisation on flat tori and lattice points in anisotropically expanding domains
Jean Lagacé
This paper is concerned with the maximisation of the k'th eigenvalue of the Laplacian amongst flat tori of unit volume in dimension d as k goes to infinity. We show that in any dim…