37 citations · 137 across the 29 of their papers we have counts for
5 papers · 1 filter
On the breathing of spectral bands in periodic quantum waveguides with inflating resonators
Lucas Chesnel, Sergei A. Nazarov
We are interested in the lower part of the spectrum of the Dirichlet Laplacian in a thin waveguide obtained by repeating periodically a pattern, its…
Generalized impedance boundary conditions with vanishing or sign-changing impedance
Lucas Chesnel, Laurent Bourgeois
We consider a Laplace type problem with a generalized impedance boundary condition of the form on a flat part of the boundary. Here …
Maxwell's equations with hypersingularities at a negative index material conical tip
Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Mahran Rihani
We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivi…
Spectrum of the Laplacian with mixed boundary conditions in a chamfered quarter of layer
Lucas Chesnel, Sergei A. Nazarov, Jari Taskinen
We investigate the spectrum of a Laplace operator with mixed boundary conditions in an unbounded chamfered quarter of layer. This problem arises in the study of the spectrum of the…
Spectrum of the Dirichlet Laplacian in a thin cubic lattice
Lucas Chesnel, Sergei A. Nazarov
We give a description of the lower part of the spectrum of the Dirichlet Laplacian in an unbounded 3D periodic lattice made of thin bars (of width ) which have a s…