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Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces

Published online by Cambridge University Press:  20 November 2018

Anders Björn ,
Jana Björn  and
Nageswari Shanmugalingam
Anders Björn
Affiliation:
Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden email: anbjo@mai.liu.se, jabjo@mai.liu.se
Jana Björn
Affiliation:
Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden email: anbjo@mai.liu.se, jabjo@mai.liu.se
Nageswari Shanmugalingam
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025 Cincinnati, OH 45221-0025, U.S.A. email: nages@math.uc.edu
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Abstract

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We study when characteristic and Hölder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and Hölder continuous functions into globally defined Sobolev functions.

Keywords

46E3531C45Characteristic functionNewtonian functionmetric spaceresolutivityHölder continuousPerron solutionp-harmonicSobolev extensionWhitney covering
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 6 , 01 December 2007 , pp. 1135 - 1153
Copyright
Copyright © Canadian Mathematical Society 2007

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