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

Chandler-Wilde, S. N., 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

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To link to this item 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:68651
Publisher:Springer

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