Shift of multiple eigenvalues under non-regular perturbations

20.03.2023 14:00 – 16:00

I will describe how the eigenvalues of some perturbed self-adjoint problems
approach those of the Dirichlet Laplacian. I will especially focus on the case
where an additional Dirichlet condition is imposed on a vanishing set inside the
domain (\small holes").
Problems of this type cannot be reduced to an analytic perturbation of the
domain. Nevertheless, eigenvalues variation can often be measured by a suitable
capacity-type functional, even when the eigenvalues are not simple. The shift
can thus be connected to the geometry of the hole and of the nodal sets. The
talk is based on several joint works with V. Felli, L. Hillairet and more recently
L. Abatangelo and P. Musolino.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Analysis Seminar"

entrée libre