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

2011/05/15 by Barceló, Juan Antonio, Fanelli, Luca, Ruiz, Alberto +1
#35J10 #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1105.2953

Abstract

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension n≥3. 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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