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

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.

arXiv comment21 pages, minor corrections

References in corpus (4)

• A First Course in Fractional Sobolev Spaces
• Trace theory for Sobolev mappings into a manifold
• Global gauges and global extensions in optimal spaces
• Lifting of fractional Sobolev mappings to noncompact covering space

Cited by in corpus (1)

• Universality of renormalisable mappings in two dimensions: the case of polar convex integrands