Calculus of Variations and Geometric Measure Theory

M. Caponi

A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces

created by caponi on 12 Sep 2025
modified on 12 Aug 2026

[BibTeX]

Published Paper

Inserted: 12 sep 2025
Last Updated: 12 aug 2026

Journal: In: Duran i Lamiel, J., Maione, A. (eds) New Frontiers in Homogenization and Fractional Calculus. Trends in Mathematics. Birkhäuser, Cham
Pages: 21
Year: 2026
Doi: 10.1007/978-3-032-20098-3_2

ArXiv: 2509.11734 PDF
Links: Journal link

Abstract:

This chapter recalls the classical formulation of the Div-Curl lemma along with its proof, and presents some possible generalizations in the fractional setting, within the framework of the Riesz fractional gradient and divergence introduced by Shieh and Spector (2015) and further developed by Comi and Stefani (2019).


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