A limiting absorption principle for the Helmholtz equation with variable coefficients

  • Federico Cacciafesta

    Università degli Studi di Padova, Italy
  • Piero D'Ancona

    Università di Roma La Sapienza, Italy
  • Renato Lucà

    Universität Basel, Switzerland
A limiting absorption principle for the Helmholtz equation with variable coefficients cover
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Abstract

We prove a limiting absorption principle for a generalized Helmholtz equation on an exterior domain with Dirichlet boundary conditions

under a Sommerfeld radiation condition at infinity. The operator is a second order elliptic operator with variable coefficients; the principal part is a small, long range perturbation of , while lower order terms can be singular and large.

The main tool is a sharp uniform resolvent estimate, which has independent applications to the problem of embedded eigenvalues and to smoothing estimates for dispersive equations.

Cite this article

Federico Cacciafesta, Piero D'Ancona, Renato Lucà, A limiting absorption principle for the Helmholtz equation with variable coefficients. J. Spectr. Theory 8 (2018), no. 4, pp. 1349–1392

DOI 10.4171/JST/229