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math.AP2022
Concentration and non-concentration of eigenfunctions of second-order elliptic operators in layered media
Assia Benabdallah, Matania Ben-Artzi, Yves Dermenjian
This work is concerned with operators of the type A = --c acting in domains := ' x (0, H) R^d x R ^+. The diffusion coefficient c > 0 depends on one coordina…
math.AP2019★ 1 cited
Concentration and confinement of eigenfunctions in a bounded open set (version 2)
Assia Benabdallah, Matania Ben-Artzi, Yves Dermenjian
Consider the Dirichlet-Laplacian in and choose another open set . The estimate $0<C_ω\leq R_ω(u):=\frac{\Vert u\Vert^{2}_{L^{2}(ω)}}{\Vert u\Ver…
math.AP2012
On the guided states of 3D biperiodic Schrödinger operators
François Bentosela, Claude Bourrely, Yves Dermenjian +1
We consider the Laplacian operator H_0 perturbed by a non-positive potential , which is periodic in two directions, and decays in the remaining one. We are interested in the cha…