Opuscula Math. 40, no. 1 (2020), 5-20

Opuscula Mathematica

On some convergence results for fractional periodic Sobolev spaces

Vincenzo Ambrosio

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 \(\Gamma\)-convergence result in the spirit of Ponce. The main theorems are obtained by using the nice structure of Fourier series.

Keywords: fractional periodic Sobolev spaces, Fourier series, \(\Gamma\)-convergence.

Mathematics Subject Classification: 42B05, 46E35, 49J45.

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  • Vincenzo Ambrosio
  • ORCID iD https://orcid.org/0000-0003-3439-1428
  • Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 12, 60131 Ancona, Italy
  • Communicated by Patrizia Pucci.
  • Received: 2019-12-15.
  • Revised: 2020-01-23.
  • Accepted: 2020-01-23.
  • Published online: 2020-02-17.
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Cite this article as:
Vincenzo Ambrosio, On some convergence results for fractional periodic Sobolev spaces, Opuscula Math. 40, no. 1 (2020), 5-20, https://doi.org/10.7494/OpMath.2020.40.1.5

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