Floating mats and sloping beaches: spectral asymptotics of the Steklov problem on polygons

Leonid Parnovski, UCL. Part of the Analysis and Applications Seminar Series.

I will discuss the asymptotic behaviour of the eigenvalues of the Steklov problem (aka Dirichlet-to-Neumann operator) on curvilinear polygons. The answer is completely unexpected and depends on the arithmetic properties of the angles of the polygon.