BMO-type seminorms and Sobolev functions

BMO-type seminorms and Sobolev functions

Following some ideas of a recent paper by Bourgain, Brezis and Mironescu, we give a representation formula of the norm of the gradient of a Sobolev function which does not make use of the distributional derivatives.

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Veröffentlicht in:ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2018-04, Vol.24 (2), p.835-847
Hauptverfasser: Fusco, Nicola, Moscariello, Gioconda, Sbordone, Carlo
Format: Artikel
Sprache:eng
Schlagworte:
46E35
BMO-type seminorms
Derivatives
Mathematical analysis
Nikol’skij spaces
Normal distribution
Sobolev functions
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Beschreibung
Zusammenfassung:Following some ideas of a recent paper by Bourgain, Brezis and Mironescu, we give a representation formula of the norm of the gradient of a Sobolev function which does not make use of the distributional derivatives.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2017023