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Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents

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Abstract

A Bourgain–Brezis–Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiting embedding theorem for these spaces fails to hold in general.

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  1. Department of Mathematics, Hanyang University, Seoul, 04763, Republic of Korea

    Minhyun Kim

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This work was supported by German Research Foundation (GRK 2235-282638148) and the research fund of Hanyang University (HY-202300000001143).

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Kim, M. Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents. Annali di Matematica 202, 2653–2664 (2023). https://doi.org/10.1007/s10231-023-01333-y

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