| Issue |
ESAIM: COCV
Volume 24, Number 2, April–June 2018
|
|
|---|---|---|
| Page(s) | 835 - 847 | |
| DOI | https://doi.org/10.1051/cocv/2017023 | |
| Published online | 13 June 2018 | |
BMO-type seminorms and Sobolev functions★
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Italy
gmoscari@unina.it; sbordone@unina.it
a Corresponding author: n.fusco@unina.it
Received:
29
May
2016
Revised:
8
March
2017
Accepted:
9
March
2017
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.
Mathematics Subject Classification: 46E35
Key words: Sobolev functions / Nikol’skij spaces / BMO-type seminorms
The authors are members of GNAMPA of the Italian Istituto Nazionale di Alta Matematica (INdAM). Part of the work of N. Fusco has been carried on at the University of Jyväskylä and supported by the FiDiPro project 2100002028. The friendly atmosphere of the Mathematics and Statistics Department of Jyväskylä is warmly acknowledged. The authors wish to thank the anonymous referee for his/her valuable comments on the first version of this paper.
© EDP Sciences, SMAI 2018
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