Concentration and non concentration for the Schrödinger equation on Zoll manifolds

In Section 3, we look for directionnal derivative of eigenvalue and we prove also that for α small enough, the minimum is not attained by the measure identically equal to zero..

Relaxed formulation for the Steklov eigenvalues: existence of optimal shapes In this section we extend the notion of the Steklov eigenvalues to arbitrary sets of finite perime- ter,

We recall that the estimates of scalar pseudo-differential calculus carry over to the L(H 0 )- valued case except the commutator estimate which holds only when the principal

We give a simple proof of a result of Martinez on resonance free domains for semiclasssical Schr¨odinger operators. I. 1 which uses only elementary pseudodiffer-

The key new ingredient for the proof is the fractal uncertainty principle, first formulated in [DyZa16] and proved for porous sets in [BoDy18].. Let (M, g) be a compact

Though the corrector problem may not have an exact solution due to non-coercivity of the Hamiltonian, homogenization suffices with an approximate corrector whose existence is

, On smoothing property of Schr¨ odinger propagators, in Functional- Analytic Methods for Partial Differential Equations (Tokyo, 1989 ), Lecture Notes in Math.. , Smoothing property

First introduced by Faddeev and Kashaev [7, 9], the quantum dilogarithm G b (x) and its variants S b (x) and g b (x) play a crucial role in the study of positive representations