In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

We apply the “black box scattering” point of view to problems in control theory for the
Schrödinger equation and in high energy eigenvalue scarring. We show how resolvent …

We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, ie the
equation∇⋅(A∇ u)+ k 2 nu=− f where both A and n are functions of position. We prove new …

We prove a local smoothing effect and Strichartz type estimates for the Schrödinger equation
on the exterior of a non-trapping obstacle. As a consequence we deduce global existence …

We consider bounds on the number of semiclassical resonances in neighbourhoods of the
size of the semiclassical parameter, h, around energy levels at which the flow is hyperbolic …

A convergence theory for the hp-FEM applied to a variety of constant-coefficient Helmholtz
problems was pioneered in the papers [35],[36],[15],[34]. This theory shows that, if the …

We show the necessity of the nontrapping condition for the plain smoothing effect (H1/2) for
the Schrödinger equation with Dirichlet boundary conditions in exterior problems. We also …

The limiting absorption principle asserts that if H is a suitable Schrödinger operator, and f
lives in a suitable weighted L 2 space (namely H^ 0, 1/2+ σ H 0, 1/2+ σ for some σ> 0 σ> 0) …

The purpose of this note is to present an alternative proof of a result by H. Smith and C.
Sogge showing that in odd dimension of space, local (in time) Strichartz estimates and …

A well known result of Jaffard states that an arbitrary region on a torus controls, in the L2
sense, solutions of the free stationary and dynamical Schroedinger equations. In this note …