A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains
Juan Antonio Barceló, Luca Fanelli, Alberto Ruiz, M. C. Vilela · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2013
We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension n ≥ 3. Using multiplier techniques in the style of Morawetz, we prove a family of a priori estimates from which the limiting absorption principle follows. Moreover, we give some standard applications to cases with an absence of embedded eigenvalues and zero resonances, under explicit conditions on the potentials.