5 citations · 6 across the 3 of their papers we have counts for
4 papers
Polynomial upper bound on interior Steklov nodal sets
Bogdan Georgiev, Guillaume Roy-Fortin
We study solutions of uniformly elliptic PDE with Lipschitz leading coefficients and bounded lower order coefficients. We extend previous results of A. Logunov concerning nodal set…
Average growth and nodal sets of eigenfunctions of the Laplacian on surfaces
Guillaume Roy-Fortin
In a recent paper, we exhibit a link between the average local growth of Laplace eigenfunctions on surfaces and the size of their nodal set. In that paper, the average local growth…
Nodal sets and growth exponents of Laplace eigenfunctions on surfaces
Guillaume Roy-Fortin
We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin that exhibits a relation between the average local growth of a Laplace eigenfunction on a closed surface and…
Wolf-Keller theorem for Neumann eigenvalues
Guillaume Poliquin, Guillaume Roy-Fortin
The classical Szego-Weinberger inequality states that among bounded planar domains of given area, the first nonzero Neumann eigenvalue is maximized by a disk. Recently, it was show…