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Sobolev Spaces on Non-Lipschitz Subsets of Rn with Application to Boundary Integral Equations on Fractal Screens

Chandler-Wilde, SN; Hewett, DP; Moiola, A; (2017) Sobolev Spaces on Non-Lipschitz Subsets of Rn with Application to Boundary Integral Equations on Fractal Screens. Integral Equations and Operator Theory , 87 (2) pp. 179-224. 10.1007/s00020-017-2342-5. Green open access

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Abstract

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of (Formula presented.). We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary.

Type: Article
Title: Sobolev Spaces on Non-Lipschitz Subsets of Rn with Application to Boundary Integral Equations on Fractal Screens
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00020-017-2342-5
Publisher version: http://dx.doi.org/10.1007/s00020-017-2342-5
Language: English
Additional information: © 2017 Springer International Publishing. The final publication is available at Springer via http://dx.doi.org/10.1007/s00020-017-2342-5
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1543156
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