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Wiener criterion on metric spaces: Boundary regularity in axiomatic and Poincaré-Sobolev spaces

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Abstract

We obtain a Wiener-type criterion for the Hölder continuity of extremal functions on general metric spaces in an abstract setting. Then we use this result to establish the boundary regularity of quasi-minimizers of the p-energy integral in the axiomatic framework of Gol’dshtein-Troyanov and also for extremal functions from the class of Poincaré-Sobolev functions.

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Authors and Affiliations

  1. Department of Mathematics and PMI, POSTECH, Pohang, Kyungbuk, 790-784, Republic of Korea

    Sergey A. Timoshin

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  1. Sergey A. Timoshin
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Correspondence to Sergey A. Timoshin.

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Timoshin, S.A. Wiener criterion on metric spaces: Boundary regularity in axiomatic and Poincaré-Sobolev spaces. Isr. J. Math. 179, 211–234 (2010). https://doi.org/10.1007/s11856-010-0079-9

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  • DOI: https://doi.org/10.1007/s11856-010-0079-9

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