Smooth topology-preserving approximations of rough domains

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• Professor John Ball, University of Oxford
• Wednesday 18 April 2012, 11:30-12:30
• MR2.

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The talk concerns bounded domains with continuous boundary. We study how the corresponding “good direction”, with respect to which the boundary is locally a graph of a continuous function, varies in a neighborhood of the boundary, and thus show how such domains can be approximated both from the inside and the outside by topologically equivalent smooth domains. The good directions form a globally-defined field that carries some topological information about the domain, which we explore. Finally we describe a surprising consequence of the study, that the domain has portions of the boundary with better regularity. This is joint work with Arghir Zarnescu.

This talk is part of the Oxbridge PDE conference series.

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