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# Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces

Published:2007-12-01
Printed: Dec 2007
• Anders Björn
• Jana Björn
• Nageswari Shanmugalingam
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## Abstract

We study when characteristic and H\"older continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and H\"older continuous functions into globally defined Sobolev functions.
 Keywords: characteristic function, Newtonian function, metric space, resolutivity, Hölder continuous, Perron solution, $p$-harmonic, Sobolev extension, Whitney covering
 MSC Classifications: 46E35 - Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems 31C45 - Other generalizations (nonlinear potential theory, etc.)