5 papers
A counterexample to Kenig's conjecture for the Laplace double-layer operator
Matthew J. Colbrook, Siavash Sadeghi
Layer potentials provide a classical approach to boundary value problems for Laplace's equation on Lipschitz domains. Kenig's 1994 spectral-radius conjecture for the double-layer o…
A sharp isoperimetric inequality for the Neumann--Poincaré operator in every dimension
Matthew J. Colbrook, Siavash Sadeghi
Let , , be a bounded connected domain with boundary of class , where . For the adjoint Neumann--Poincaré operator , no…
A computer-assisted counterexample to the planar Berenstein conjecture
Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants
Recent work of Colbrook and Stepaniants produced the first counterexamples to the planar Pompeiu and Schiffer conjectures and introduced the conformal fixed-disc, disk-polynomial,…
Integral Equation Methods for Scattering by Multifractal Obstacles
Simon N. Chandler-Wilde, Gabriel Claret, David P. Hewett +2
Caetano et al. (Proc. R. Soc. A. 481:20230650, 2025) have proposed a formulation for sound-soft acoustic scattering by a compact scatterer O Rn, in which the scattered fi…
Integral equation methods for scattering by general compact obstacles: wavenumber-explicit estimates
Simon N. Chandler-Wilde, Siavash Sadeghi
There has been significant recent interest in understanding the dependence on the wavenumber, , of boundary integral operators (BIOs), supported on some set $Γ\subset \mathbb{R}…