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

Shaoguang Shi and Lei Zhang

Mathematische Nachrichten, 2020, vol. 293, issue 11, 2233-2247

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.

Date: 2020
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https://doi.org/10.1002/mana.201800438

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