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Fine continuity on metric spaces

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Abstract

We obtain pointwise estimates for solutions of obstacle problems on metric measure spaces and prove that p-superharmonic functions are p-finely continuous. Consequently, we show that p-quasicontinuous functions are p-finely continuous at p-quasievery point. As a byproduct, we obtain the sufficiency part of the Wiener criterion in metric spaces without the assumption of linear local connectedness.

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Authors and Affiliations

  1. Department of Mathematics, Linköpings universitet, 581 83, Linköping, Sweden

    Jana Björn

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  1. Jana Björn
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Correspondence to Jana Björn.

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The author was supported by the Swedish Research Council.

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Björn, J. Fine continuity on metric spaces. manuscripta math. 125, 369–381 (2008). https://doi.org/10.1007/s00229-007-0154-7

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  • DOI: https://doi.org/10.1007/s00229-007-0154-7

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