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Estimées résolvantes uniformes pour une équation de Helmholtz non dissipative

Uniform resolvent estimates for a non-dissipative Helmholtz equation

Julien Royer
Estimées résolvantes uniformes pour une équation de Helmholtz non dissipative
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  • Année : 2014
  • Fascicule : 4
  • Tome : 142
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 35J10, 47A10, 47A55, 47B44, 47G30, 81Q20
  • Pages : 591-633
  • DOI : 10.24033/bsmf.2674
We study the high frequency limit for a non-selfadjoint Helmholtz equation. This equation models the propagation of the electromagnetic field of a laser in an inhomogeneus material medium with non-constant absorption index. In this paper the absorption index can take negative values and we only use a damping condition on the ical limit of the problem. In this setting we first prove the absence of eigenvalue on the upper half-plane and close to an energy which satisfies this damping assumption. Then we generalize the resolvent estimates of Robert-Tamura and prove the limiting absorption principle. We finally study the semi ical measures of the solution when the source term concentrates on a bounded submanifold of $\mathbb R ^n$.
Non-selfadjoint operators, resolvent estimates, limiting absorption principle, Helmholtz equation, semi ical measures.
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