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 …

It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

We study asymptotic distribution of eigenvalues of the Laplacian on a bounded domain in ℝ
n. Our main results include an explicit remainder estimate in the Weyl formula for the …

We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet
Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex …

We apply recent results by the authors to obtain bounds on remainder terms of the Dirichlet
Laplace eigenvalue counting function for domains that can be realised as countable unions …

We consider differential operators defined as Friedrichs extensions of quadratic forms with
non-smooth coefficients. We prove a two-term optimal asymptotic for the Riesz means of …

We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded
domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of …

We consider operators acting in L 2 (R d) with d≥ 3 that locally behave as a magnetic
Schrödinger operator. For the magnetic Schrödinger operators, we suppose the magnetic …

We obtain estimates for the counting function of the Neumann Laplacian on a planar domain
bounded by the graph of a lower semicontinuous L1-function. These estimates imply …

We consider operators acting in $ L^ 2 (\mathbb {R}^ d) $ with $ d\geq3 $ that locally behave
as a magnetic Schr\" odinger operator. For the magnetic Schr\" odinger operators we …