We establish a limiting absorption principle for Dirichlet Laplacians in
quasi-cylindrical domains. Outside a bounded set these domains can be
transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet
Laplacians model quantum or acoustically-soft waveguides associated with
quasi-cylindrical domains. We construct a uniquely solvable problem with
perfectly matched layers of finite length. We prove that solutions of the
latter problem approximate outgoing or incoming solutions with an error that
exponentially tends to zero as the length of layers tends to infinity. Outgoing
and incoming solutions are characterized by means of the limiting absorption
principle.Comment: to appear in SIAM Journal on Mathematical Analysi
