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

Bulanyi, Bohdan;Van Schaftingen, Jean
(2025) Journal of Functional Analysis — Vol. 288, n° 1, p. 110681 (2025)

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Given m∈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(Sm,N), a map U:Bm+1→N whose trace is u and which satisfies an exponential weak-type Sobolev estimate. The result and its proof carry on to the extension to a half-space of maps on its boundary hyperplane and to the extension to the hyperbolic space of maps on its boundary sphere at infinity.
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Bulanyi, B., & Van Schaftingen, J. (2025). Singular extension of critical Sobolev mappings under an exponential weak-type estimate. Journal of Functional Analysis, 288(1), 110681. https://doi.org/10.1016/j.jfa.2024.110681 (Original work published 2025)