Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials
Published online by Cambridge University Press: 24 July 2014
Abstract
We study the Helmholtz equation
in ℝd with magnetic and electric potentials that are singular at the origin and decay at ∞. 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 multiplier technique of Morawetz type.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 4 , August 2014 , pp. 857 - 890
- Copyright
- Copyright © Royal Society of Edinburgh 2014
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