Approximation of Holder continuous homeomorphisms by piecewise affine homeomorphisms

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dc.creatorBellido, Jose C.
dc.creatorMora-Corral, Carlos
dc.date2008-06-20
dc.date.accessioned2026-07-07T09:45:52Z
dc.date.available2026-07-07T09:45:52Z
dc.descriptionThis paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to R^2 that is globally Holder continuous of exponent α, and whose inverse is also globally Holder continuous of exponent αcan be approximated in the Holder norm of exponent βby piecewise affine homeomorphisms, for some βthat only depends on α. The proof is constructive. We adapt the proof of simplicial approximation in the supremum norm, and measure the side lengths and angles of the triangulation over which the approximating homeomorphism is piecewise affine. The approximation in the supremum norm, and a control on the minimum angle and on the ratio between the maximum and minimum side lengths of the triangulation suffice to obtain approximation in the Holder norm.
dc.description46 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0806.3366
dc.identifierhttp://arxiv.org/abs/0806.3366
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163341
dc.subjectClassical Analysis and ODEs
dc.subjectFunctional Analysis
dc.subject57Q55
dc.titleApproximation of Holder continuous homeomorphisms by piecewise affine homeomorphisms
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