Séminaire : High frequency uniform resolvent estimates for the magnetic Laplacian

Date/heure
2 juin 2023
11:00 - 12:00

Lieu
Salle de séminaires Metz

Oratrice ou orateur
Viviana Grasselli (Université Toulouse III - Paul Sabatier, Toulouse)

Catégorie d'évènement
Séminaire EDP, Analyse et Applications (Metz)

We consider the magnetic Laplacian on non compact Riemannian manifolds which have ends of infinite volume, including for example asymptotically conical or hyperbolic manifolds. We will show how we can obtain uniform estimates for the boundary values of the resolvent of this operator in the case of high frequencies. These estimates hold in spaces with optimal weights and imply boundedness of the limiting resolvent in $L^2$ spaces with weights decaying faster than the inverse square root. In particular in this talk we will show how we can generalize a work by Cardoso and Vodev (’02) when adding perturbations of order one and zero and considering optimal weights. We will also focus on the aspects of the proof which are frequency independent.