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Singular extension of critical Sobolev mappings under an exponential weak-type estimate (2309.12874v2)
Published 22 Sep 2023 in math.AP, math.CA, and math.FA
Abstract: Given $m \in \mathbb{N} \setminus {0}$ and a compact Riemannian manifold $\mathcal{N}$, we construct for every map $u$ in the critical Sobolev space $W{m/(m + 1), m + 1} (\mathbb{S}m, \mathcal{N})$, a map $U : \mathbb{B}{m + 1} \to \mathcal{N}$ 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.