18 citations · 90 across the 16 of their papers we have counts for
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Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
Pierre Bérard, Bernard Helffer, Rola Kiwan
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp…
Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains. Application to the Extended Courant Property
Pierre Bérard, Bernard Helffer
In this paper, we prove that the Extended Courant Property fails to be true for certain smooth, strictly convex domains with Neumann boundary condition: there exists a linear combi…
On Courant's nodal domain property for linear combinations of eigenfunctions, Part II
Pierre Bérard, Bernard Helffer
Generalizing Courant's nodal domain theorem, the "Extended Courant property" is the statement that a linear combination of the first eigenfunctions has at most nodal domain…
Sturm's theorem on zeros of linear combinations of eigenfunctions
Pierre Bérard, Bernard Helffer
Motivated by recent questions about the extension of Courant's nodal domain theorem, we revisit a theorem published by C. Sturm in 1836, which deals with zeros of linear combinatio…
The weak Pleijel theorem with geometric control
Pierre Bérard, Bernard Helffer
Let , be a bounded open set, and denote by , the eigenvalues of the Dirichlet Laplacian arranged in nondecreasing order, with mul…
On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern --
Pierre Bérard, Bernard Helffer
In the case of the sphere and the square, Antonie Stern (1925) claimed in her PhD thesis the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contai…