Jean Van Schaftingen

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math.AP2024

Injective ellipticity, cancelling operators, and endpoint Gagliardo-Nirenberg-Sobolev inequalities for vector fields

Jean Van Schaftingen

Although Ornstein's nonestimate entails the impossibility to control in general all the $L^{1}$ -norm of derivatives of a function by the $L^{1}$ -norm of a constant coefficient homogene…

math.AP2024

Singular extension of critical Sobolev mappings under an exponential weak-type estimate

Bohdan Bulanyi, Jean Van Schaftingen

Given $m \in N ∖ {0}$ and a compact Riemannian manifold $N$ , we construct for every map $u$ in the critical Sobolev space $W^{m/(m + 1), m + 1} (\mathb…