Speaker
Alix Deleporte, Université Paris-Saclay
Abstract
In this talk, I will present the techniques used in a work in progress with J. Lagacé (KCL) and L. Parnovski (UCL) about Steklov eigenvalue asymptotics for rough 2D domains. After conformal mapping to the circle and a unitary conjugation by length-arc parametrisation, the operator under study is close to the Dirichlet-to-Neumann map on the disk. To analyse the precise regularising properties of the remainder and the asymptotics of its matrix elements, we notably introduce a Sobolev space version of the majorant series technique wildly used in complex analysis.