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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Copyright © 2008 by Academia Scientiarum Fennica