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<p>We explore the asymptotic behavior of families of Bourgain–Brezis–Mironescu type nonlocal functionals for mappings from certain metric measure spaces to arbitrary metric spaces. As the first outcome, we obtain a characterization of Sobolev maps and of maps of bounded variation via such functionals. As the second outcome, we establish precise expressions for the limits of such functionals for Sobolev maps. All this provides an extension for several results of the Bourgain–Brezis–Mironescu type to the entirely singular setting.</p>

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Asymptotic Relations of the Bourgain–Brezis–Mironescu Type for Mappings Between Singular Spaces

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Roman Oleinik

摘要

We explore the asymptotic behavior of families of Bourgain–Brezis–Mironescu type nonlocal functionals for mappings from certain metric measure spaces to arbitrary metric spaces. As the first outcome, we obtain a characterization of Sobolev maps and of maps of bounded variation via such functionals. As the second outcome, we establish precise expressions for the limits of such functionals for Sobolev maps. All this provides an extension for several results of the Bourgain–Brezis–Mironescu type to the entirely singular setting.