Seminar Analysis: Laura V. Spinolo (IMATI-CNR, Pavia)

Spectral stability estimates for the Laplace operator with either Dirichlet or Neumann boundary conditions

The talk will focus on the eigenvalue problem for the Laplace operator defined in an open and bounded domain, with homogenous conditions of either Dirichlet or Neumann type assigned at the boundary. Under fairly weak regularity assumptions on the domain, the problem admits a diverging sequence of nonnegative eigenvalues. I will discuss some new quantitative estimates controlling how each of the eigenvalues change when the domain is perturbed. These estimates apply to Lipschitz and to so-called Reifenberg-flat domains.  The proof is based on an abstract lemma which applies to both the Neumann and the Dirichlet problem and which could be applied to other classes of domains.

The talk will be based on joint works with A. Lemenant and E. Milakis.

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