A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains

Details A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains

2011-05-15

arxiv.org/abs/1105.2953v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension $n\geq3$. We prove, by multiplier techniques in the sense of Morawetz, a family of a priori estimates from which the limiting absorption principle follows. Moreover, we give some standard applications to the absence of embedded eigenvalues and zero-resonances, under explicit conditions on the potentials.

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