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

Shi Shaoguang | Zendy; Zhang Lei | Zendy

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

Author(s) -

Shi Shaoguang,

Zhang Lei

Publication year - 2020

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201800438

Subject(s) - mathematics , laplace transform , sobolev space , fractional calculus , bounded function , mathematical analysis , characterization (materials science) , dual (grammatical number) , zero (linguistics) , linguistics , philosophy , art , materials science , literature , nanotechnology

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.

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