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

Published online by Cambridge University Press:  30 January 2013

Juan Antonio Barceló
Affiliation:
ETSI de Caminos, Universidad Politécnica de Madrid, 28040 Madrid, Spain (juanantonio.barcelo@upm.es)
Luca Fanelli
Affiliation:
Departamento de Matemáticas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain (luca.fanelli@ehu.es)
Alberto Ruiz
Affiliation:
Departamento de Matemáticas, Universidad Autóonoma de Madrid, 28049 Madrid, Spain (alberto.ruiz@uam.es)
Maricruz Vilela
Affiliation:
Departamento de Matemática Aplicada, Universidad de Valladolid, Plaza Santa Eulalia 9 y 11, Segovia, Spain (maricruz@dali.eis.uva.es)

Abstract

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension n ≥ 3. Using multiplier techniques in the style of Morawetz, we prove a family of a priori estimates from which the limiting absorption principle follows. Moreover, we give some standard applications to cases with an absence of embedded eigenvalues and zero resonances, under explicit conditions on the potentials.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2013

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