6 papers
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…
Helmholtz transmission problem and intrinsic impedance scattering problem on extension domains
Gabriel Claret
We consider a transmission problem for the Helmholtz equation with a fixed, positive wavenumber across the boundary of an extension domain. Such a boundary can be Lipschitz, fracta…
Poincar{é}-Steklov operator and Calder{ó}n's problem on extension domains
Gabriel Claret, Michael Hinz, Anna Rozanova-Pierrat
We consider Calder{ó}n's problem on a class of Sobolev extension domains containing non-Lipschitz and fractal shapes. We generalize the notion of Poincar{é}-Steklov (Dirichlet-to-N…
Convergence of layer potentials and Riemann-Hilbert problem on extension domains
Gabriel Claret, Anna Rozanova-Pierrat, Alexander Teplyaev
We prove the convergence of layer potential operators for the harmonic transmission problem over a sequence of converging two-sided extension domains. Consequently, the Neumann-Poi…
Layer potential operators for transmission problems on extension domains
Gabriel Claret, Michael Hinz, Anna Rozanova-Pierrat +1
We use the well-posedness of transmission problems on classes of two-sided Sobolev extension domains to give variational definitions for (boundary) layer potential operators and Ne…
Existence of optimal shapes for heat diffusions across irregular interfaces
Gabriel Claret, Anna Rozanova-Pierrat
We consider a heat transmission problem across an irregular interface -- that is, non-Lipschitz or fractal -- between two media (a hot one and a cold one). The interface is modelle…