On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces (Q2039127)
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scientific article; zbMATH DE number 7367172
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces |
scientific article; zbMATH DE number 7367172 |
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On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces (English)
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2 July 2021
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Summary: 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 [\textit{J.~Fernández Bonder} and \textit{A.~M. Salort}, J. Funct. Anal. 277, No.~2, 333--367 (2019; Zbl 1426.46018)], where Young functions satisfying the \(\Delta_2\) 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.
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fractional Orlicz-Sobolev spaces
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limit of smoothness parameters
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Orlicz-Sobolev spaces
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functions of bounded variation
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