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.
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.File in questo prodotto:
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