Abstract
We consider the problem of extending functions to functions for . We assume belongs to the critical space and we construct a -controlled extension . The Lorentz–Sobolev space is optimal for such controlled extension. Then we use these results to construct global controlled gauges for -connections over trivial -bundles in dimensions. This result is a global version of the local Sobolev control of connections obtained by K. Uhlenbeck.
Citation
Mircea Petrache. Tristan Rivière. "Global gauges and global extensions in optimal spaces." Anal. PDE 7 (8) 1851 - 1899, 2014. https://doi.org/10.2140/apde.2014.7.1851
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