Radiating and non-radiating sources in elasticity

Abstract

In this work, we study the inverse source problem of a fixed frequency for the Navier equation. We investigate non-radiating external forces. If the support of such a force has a convex or non-convex corner or edge on its boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: an energy identity and a new type of exponential solution for the Navier equation.