2 citations · 4 across the 10 of their papers we have counts for
12 papers
Pleijel's theorem for Schrödinger operators
Philippe Charron, Corentin Léna
We are concerned in this paper with the real eigenfunctions of Schrödinger operators. We prove an asymptotic upper bound for the number of their nodal domains, which implies in par…
A theory of spectral partitions of metric graphs
James B. Kennedy, Pavel Kurasov, Corentin Léna +1
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus…
Concrete method for recovering the Euler characteristic of quantum graphs
Corentin Léna, Andrea Serio
Trace formulas play a central role in the study of spectral geometry and in particular of quantum graphs. The basis of our work is the result by Kurasov which links the Euler chara…
Asymptotic behavior of -capacities and singular perturbations for the Dirichlet-Laplacian
Laura Abatangelo, Virginie Bonnaillie-Noël, Corentin Léna +1
In this paper we study the asymptotic behavior of -capacities of small sets and its application to the analysis of the eigenvalues of the Dirichlet-Laplacian on a bounded planar…
On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains--with some numerics--
Bernard Helffer, Thomas Hoffmann-Ostenhof, François Jauberteau +1
We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R2 for which the second eigenvalue of the D…
Upper bounds for Courant-sharp Neumann and Robin eigenvalues
Katie Gittins, Corentin Léna
We consider the eigenvalues of the Laplacian on an open, bounded, connected set in with boundary, with a Neumann boundary condition or a Robin boundary conditi…
Eigenvalue variation under moving mixed Dirichlet-Neumann boundary conditions and applications
Laura Abatangelo, Veronica Felli, Corentin Léna
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…
Examples of spectral minimal partitions
Corentin Léna
We study a minimal partition problem on the flat rectangular torus. We give a partial review of the existing literature, and present some numerical and theoretical work recently pu…
Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions
Corentin Léna
In this paper, we show that equality in Courant's nodal domain theorem can only be reached for a finite number of eigenvalues of the Neumann Laplacian, in the case of an open, boun…
Courant-sharp eigenvalues of the three-dimensional square torus
Corentin Léna
In this paper, we determine, in the case of the Laplacian on the flat three-dimensional torus , all the eigenvalues having an eigenfunction which satisfi…
On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori
Corentin Léna
In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tor…
Courant-sharp eigenvalues of a two-dimensional torus
Corentin Léna
In this paper, we determine, in the case of the Laplacian on the flat two-dimensional torus (R/Z) 2 , all the eigenvalues having an eigenfunction which satisfies Courant's theorem…