Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Hewett, D. P. and 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. ISSN 1420-8989 doi: 10.1007/s00020-017-2342-5

Abstract/Summary

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/68651
Identification Number/DOI	10.1007/s00020-017-2342-5
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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