On the limit as $s \to 1^-$ of possibly non-separable fractional Orlicz–Sobolev spaces

Angela Alberico; Andrea Cianchi; Luboš Pick; Lenka Slavíková

doi:10.4171/rlm/918

JournalsrlmVol. 31, No. 4pp. 879–899

On the limit as $s \to 1^{-}$ of possibly non-separable fractional Orlicz–Sobolev spaces

Angela Alberico
Consiglio Nazionale delle Ricerche, Napoli, Italy
Andrea Cianchi
Università di Firenze, Italy
Luboš Pick
Charles University, Prague, Czechia
Lenka Slavíková
University of Bonn, Germany, and Charles University, Prague, Czechia

$On the limit as $s \to 1^-$ of possibly non-separable fractional Orlicz–Sobolev spaces cover$

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Abstract

Extended versions of the Bourgain–Brezis–Mironescu theorems on the limit as $s \to 1^{-}$ of the Gagliardo–Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz–Sobolev spaces built upon general Young functions, and complement those of [13], where Young functions satisfying the $Δ_{2}$ and the $\nabla_{2}$ conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation.

Cite this article

Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková, On the limit as $s \to 1^{-}$ of possibly non-separable fractional Orlicz–Sobolev spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 879–899

DOI 10.4171/RLM/918