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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.