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Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

Published online by Cambridge University Press:  24 July 2014

Miren Zubeldia
Miren Zubeldia*
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Spain, miren.zubeldia@ehu.es
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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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