Quantitative Stability with respect to domain perturbation for the Laplacian
Antoine Lemenant,
(Laboratoire Jacques Louis Lions, Université Paris Diderot)
04/07/2013
In this talk we will describe a method to quantify the differences of two solution for the Dirichlet (or Neumann) problem in two open sets relatively close to each others. For instance we will estimate the difference of the spectrum of the Dirichlet (or Neumann) Laplacian of two different domains with respect to the Hausdorff distance between those domains. This will be achieved under a certain (weak) regularity assumption on the boundary of the domains : Reifenberg-flat, which includes for instance Lipschitz domains. This is a work in common with E. Milakis (Cyprus) and L. V. Spinolo (Pavia).