Séminaire OrléansSpectral Cluster estimates on polygonal domains
Jeremy Marzuola (U. North Carolina)
Thursday 25 June 2015 14:00 - Orléans - Salle de Séminaire
In joint work with Matt Blair and Austin Ford, we look at the $L^p$ bounds on eigenfunctions for polygonal domains (or more generally Euclidean surfaces with conic singularities) by analysis of the wave operator on the flat Euclidean cone. Using explicit oscillatory integrals and relying on the fundamental solution to the wave equation in geometric regions related to flat wave propagation and diffraction by the cone point, we can prove spectral cluster estimates equivalent to those in works on smooth Riemannian manifolds.