5 citations · 35 across the 33 of their papers we have counts for
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Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field
Bernard Helffer, Zeinab Karaki
In continuation of a former work by the first author with F. Nier (2009) and of a more recent work by the second author on the torus (2019), we consider the Kramers-Fokker-Planck o…
Spectral flow for pair compatible equipartitions
Bernard Helffer, Mikael Persson Sundqvist
We show that a recent spectral flow approach proposed by Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be ext…
An Euler-type formula for partitions of the Möbius strip
Pierre Bérard, Bernard Helffer
The purpose of this note is to prove an Euler-type formula for partitions of the Möbius strip. This formula was introduced in our joint paper with R.~Kiwan, "Courant-sharp property…
Magnetic confinement for the 3D Robin Laplacian
Bernard Helffer, Ayman Kachmar, Nicolas Raymond
We determine accurate asymptotics of the lowest eigenvalue for the Laplace operator with a smooth magnetic field and Robin boundary conditions in a smooth 3D domain, when the Robin…
Courant-sharp Robin eigenvalues for the square: the case of negative Robin parameter
Katie Gittins, Bernard Helffer
We consider the cases where there is equality in Courant's nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we trea…