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Characterizations of interior polar sets for the degenerate p-parabolic equation

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Abstract

This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain interior polar sets can be characterized by sets of zero nonlinear parabolic capacity. Furthermore we prove that zero capacity sets are removable for bounded supersolutions and that sets of zero capacity have a relation to a certain parabolic Hausdorff measure.

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Authors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University School of Science, 00076, Aalto, Finland

    Benny Avelin & Olli Saari

  2. Department of Mathematics, Uppsala University, 751 06, Uppsala, Sweden

    Benny Avelin

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  1. Benny Avelin
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  2. Olli Saari
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Correspondence to Benny Avelin.

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Avelin, B., Saari, O. Characterizations of interior polar sets for the degenerate p-parabolic equation. J. Evol. Equ. 17, 827–848 (2017). https://doi.org/10.1007/s00028-016-0339-1

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