Sommerfeld radiation condition and a priori estimates for Helmholtz equation with magnetic potential

Details Sommerfeld radiation condition and a priori estimates for Helmholtz equation with magnetic potential Sommerfeld radiation condition and a priori estimates for Helmholtz equation with magnetic potential

2011-04-21

arxiv.org/abs/1104.4237v2

Mathematics

Analysis of PDEs

Scientific paper

We study the following Helmholtz equation with an electromagnetic potential \label{abstract} (\nabla +ib(x))^{2} u + \lambda u + p(x) u + Q(x) u = f(x)\notag in $\Rd$. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multipliers technique of Morawetz-type.

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