5 citations · 5 across the 7 of their papers we have counts for
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Capacity estimates and improved lower bounds for the inner radius of nodal domains
Philippe Charron
We show that for every closed, smooth manifold of dimension , there exists such that any nodal domain of a Laplace eigenfunction with eigenvalue contain…
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…
Non-boundedness of the number of super level domains of eigenfunctions
Pierre Bérard, Philippe Charron, 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…
Pleijel's theorem for Schrödinger operators with radial potentials
Philippe Charron, Bernard Helffer, Thomas Hoffmann-Ostenhof
In 1956 . Pleijel gave his celebrated theorem showing that the inequality in Courant's theorem on the number of nodal domains is strict for large eigenvalues of the Laplacian. T…
A Pleijel-type theorem for the quantum harmonic oscillator
Philippe Charron
We prove a Pleijel-type theorem for the asymptotic behaviour of the number of nodal domains of eigenfunctions of the quantum harmonic oscillator in any dimension.