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Dual characterization of fractional capacity via solution of fractional p‐Laplace equation

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  • Shaoguang Shi
  • Lei Zhang

Abstract

In terms of weak solutions of the fractional p‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p‐Laplace equation.

Suggested Citation

  • Shaoguang Shi & Lei Zhang, 2020. "Dual characterization of fractional capacity via solution of fractional p‐Laplace equation," Mathematische Nachrichten, Wiley Blackwell, vol. 293(11), pages 2233-2247, November.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:11:p:2233-2247
    DOI: 10.1002/mana.201800438
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