This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus
on establishing when equivalence of norms is in fact equality of norms in the key results of …

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in
the sense that the bilinear forms cannot be bounded below by a positive multiple of the …

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of
R^ n R n. We investigate the extent to which the properties of these spaces, and the relations …

We propose and analyse a hybrid numerical–asymptotic boundary element method (BEM)
for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of …

We develop a spectral method for solving univariate singular integral equations over unions
of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the …

We consider time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-
hard (Neumann) screens embedded in R^n for n= 2 or 3. In contrast to previous studies in …

We study the classical first-kind boundary integral equation reformulations of time-harmonic
acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens. We …

This paper concerns the following question: given a subset E of ℝ n with empty interior and
an integrability parameter 1< p<∞, what is the maximal regularity s∈ ℝ for which there …

We study time-harmonic scattering in ℝ n (n= 2, 3) by a planar screen (a “crack” in the
context of linear elasticity), assumed to be a non-empty bounded relatively open subset Γ of …

We describe some recent advances in the numerical solution of acoustic scattering
problems. A major focus of the paper is the efficient solution of high frequency scattering …