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. 1349–1392DOI 10.4171/JST/229