How to hear the corners of a drum
Paper i proceeding, 2019

We prove that the existence of corners in a class of planar domain, which includes all simply connected polygonal domains and all smoothly bounded domains, is a spectral invariant of the Laplacian with both Neumann and Robin boundary conditions. The main ingredient in the proof is a locality principle in the spirit of Kac’s “principle of not feeling the boundary,” but which holds uniformly up to the boundary. Albeit previously known for Dirichlet boundary condition, this appears to be new for Robin and Neumann boundary conditions, in the geometric generality presented here. For the case of curvilinear polygons, we describe how the same arguments using the locality principle are insufficient to obtain the analogous result. However, we describe how one may be able to harness powerful microlocal methods and combine these with the locality principles demonstrated here to show that corners are a spectral invariant; this is current work-in-progress (Nursultanov et al., Preprint).


Julie Rowlett

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Medet Nursultanov

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

David Sher

DePaul University

Matrix Annals

Vol. 2017 243-278

Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book
Matrix Research Institute , Australia,




Matematisk analys



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