Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 33, 2008, 605-624

REMOVABLE SETS FOR HÖLDER CONTINUOUS p-HARMONIC FUNCTIONS ON METRIC MEASURE SPACES

Tero Mäkäläinen

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; tjmakala 'at' jyu.fi

Abstract. We show that sets of weighted (-p + \alpha(p - 1))-Hausdorff measure zero are removable for \alpha-Hölder continuous Cheeger p-harmonic functions. The result is optimal for small \alpha. Moreover, we obtain the optimal Hölder continuity of p-supersolutions in terms of the associated Riesz measures.

2000 Mathematics Subject Classification: Primary 31C45, 31C05, 35J60.

Key words: p-harmonic, metric space, removable sets, supersolutions, superharmonic, equations involving measures, balayage.

Reference to this article: T. Mäkäläinen: Removable sets for Hölder continuous p-harmonic functions on metric measure spaces. Ann. Acad. Sci. Fenn. Math. 33 (2008), 605-624.

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