University of Lisbon, Portugal
Mon 2nd Sep 2019, 12-1pm, Carslaw Room 829 (AGR)
We are interested in the eigenvalues of the Laplacian on a bounded domain with boundary conditions of the form , where is the outer unit normal to the boundary and should be considered a parameter on which the eigenvalues depend.
For positive this operator, and in particular its eigenvalues, interpolate in a strong sense between those of the Neumann () and Dirichlet (formally ) Laplacians. In recent years, however, the case of large negative has been studied intensively, and in particular the asymptotics of the eigenvalues in the singular limit is well understood: there is a sequence of eigenvalues which diverges like , independently of the geometry of the domain, while any non-divergent eigenvalues converge to points in the spectrum of the Dirichlet Laplacian.
Here, after giving a brief overview of what is known for real , we will present a number of new results for the corresponding problem when is a (usually large) complex parameter. This is based on ongoing joing work with Sabine Bögli (Imperial College London) and Robin Lang (University of Stuttgart).
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Enquiries to Daniel Hauer or Daniel Daners.