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.
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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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