Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces

Björn, Anders ; Björn, Jana ; Shanmugalingam, Nageswari

Canadian journal of mathematics, Tome 59 (2007) no. 6, pp. 1135-1153

Résumé

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.

Détail

DOI : 10.4153/CJM-2007-049-7

Mots-clés : 46E35, 31C45, Characteristic function, Newtonian function, metric space, resolutivity, Hölder continuous, Perron solution, p-harmonic, Sobolev extension, Whitney covering

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