BMO-type seminorms and Sobolev functions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 835-847.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017023
Classification : 46E35
Mots-clés : Sobolev functions, Nikol’skij spaces, BMO-type seminorms
Fusco, Nicola 1 ; Moscariello, Gioconda 1 ; Sbordone, Carlo 1

1 
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     title = {BMO-type seminorms and {Sobolev} functions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Fusco, Nicola; Moscariello, Gioconda; Sbordone, Carlo. BMO-type seminorms and Sobolev functions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 835-847. doi : 10.1051/cocv/2017023. http://www.numdam.org/articles/10.1051/cocv/2017023/

[1] L. Ambrosio, H. Brezis, J. Bourgain and A. Figalli, BMO-type norms related to the perimeter of sets. Commun. Pure Appl. Math. 69 (2016) 1062–1086 | DOI | MR | Zbl

[2] L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monogr. The Clarendon Press, Oxford University Press, New York (2000) | MR | Zbl

[3] L. Beck, Elliptic regularity theory. Lecture Notes of the Unione Matematica Italiana Springer International Publishing, Switzerland (2016) | DOI | MR

[4] J. Bourgain, H. Brezis and P. Mironescu, A new function space and applications. J. Eur. Math. Soc. 6 (2015) 2083–2101 | DOI | MR | Zbl

[5] G. De Philippis, N. Fusco and A. Pratelli, On the approximation of SBV functions. To appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., also available at http://cvgmt.sns.it/paper/3235/. | MR

[6] N. Fusco, G. Moscariello and C. Sbordone, A formula for the total variation of SBV functions. J. Funct. Anal. 270 (2016) 419–446 | DOI | MR | Zbl

[7] H. Hadwiger, Gitterperiodische Punktmengen und Isoperimetrie. Monatsh. Math. 76 (1972) 410–418 | DOI | MR | Zbl

[8] J. Kristensen and G. Mingione, The singular set of ω-minima. Arch. Ration. Mech. Anal. 177 (2005) 93–114 | DOI | MR | Zbl

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