Semiclassical measure for the solution of the Helmholtz equation with an unbounded source

Abstract

We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of Rⁿ. We prove that the solution has a unique semi-classical measure, which is precisely described in terms of the classical properties of the problem. This result is already known when the micro-support of the source is bounded, we now consider the general case.