On the growth properties of interior transmission eigenfunctions near corners

Abstract

We investigate the localization and vanishing of $L^2$ interior transmission eigenfunctions at corners. Past numerical computations suggest that these eigenfunctions localize at non-convex corners. This phenomenon has, however, not been proven theoretically. We show that localization does indeed occur for some eigenfunctions at a non-convex corner. We also investigate the vanishing of interior transmission eigenfunctions at a convex corner. We prove that these eigenfunctions vanish at convex corners with reduced smoothness assumptions compared to earlier results.