Antoine Detaille

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20202025

most citedA decomposition for Borel measures

μ \leq H^{s}

1 citations · 1 across the 7 of their papers we have counts for

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math.FA2025

A surprising threshold for the validity of the method of singular projection

Antoine Detaille

Given a compact manifold $N$ embedded into $R^{ν}$ and a projection $P$ that retracts $R^{ν}$ except a singular set of codimension $ℓ$ onto $ \…

math.FA2024

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds

Antoine Detaille, Jean Van Schaftingen

For any integer $p \geq 2$ , we construct a compact Riemannian manifold $N$ such that if $dim M > p$ , there is a map in the Sobolev space of mappings $ W^…

math.FA2024

An improved dense class in Sobolev spaces to manifolds

Antoine Detaille

We consider the strong density problem in the Sobolev space $W^{s, p} (Q^{m}; N)$ of maps with values into a compact Riemannian manifold $N$ . It is known, from…

math.FA2023

A complete answer to the strong density problem in Sobolev spaces with values into compact manifolds

Antoine Detaille

We consider the problem of strong density of smooth maps in the Sobolev space $W^{s, p} (Q^{m}; N)$ , where $0 < s < + \infty$ , $1 \leq p < + \infty$ , $Q^{m}$ is the un…