Equi-integrable approximation of Sobolev mappings between manifolds

Jean Van Schaftingen

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arXiv · 2511.20064

Equi-integrable approximation of Sobolev mappings between manifolds

Jean Van Schaftingen

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Abstract

We show that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable $W^{1, p}$-Sobolev energy can always be strongly approximated by smooth maps, giving a counterpart of Hang's density result in $W^{1, 1}$ for the Sobolev space $W^{1, p}$ with integer $p \ge 2$. Our result extends to higher-order Sobolev spaces and is straightforward in fractional Sobolev spaces. We also provide a proof based on the weak continuity of Jacobians in the cases where the cohomological criterion of Bethuel, Demengel, Colon and H\'elein applies.

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Jean Van Schaftingen. 2025-11-25. Equi-integrable approximation of Sobolev mappings between manifolds. https://arxiv.org/abs/2511.20064

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