In this note we extend the well-known limiting formulas due to Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova, to the setting of fractional Sobolev spaces on the torus. We also give a Γ-convergence result in the spirit of Ponce. The main theorems are obtained by using the nice structure of Fourier series.

On some convergence results for fractional periodic Sobolev spaces / Ambrosio, V.. - In: OPUSCULA MATHEMATICA. ROCZNIK AKADEMIA GÓRNICZO-HUTNICZA IM. STANISłAWA STASZICA. - ISSN 1232-9274. - 40:1(2020), pp. 5-20. [10.7494/OpMath.2020.40.1.5]

On some convergence results for fractional periodic Sobolev spaces

Ambrosio V.
2020-01-01

Abstract

In this note we extend the well-known limiting formulas due to Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova, to the setting of fractional Sobolev spaces on the torus. We also give a Γ-convergence result in the spirit of Ponce. The main theorems are obtained by using the nice structure of Fourier series.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/278513
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