Volume 24, Number 2, April–June 2018
|Page(s)||835 - 847|
|Published online||13 June 2018|
BMO-type seminorms and Sobolev functions★
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Italy
a Corresponding author: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.