Analysis & PDE
- Anal. PDE
- Volume 7, Number 8 (2014), 1851-1899.
Global gauges and global extensions in optimal spaces
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.
Anal. PDE, Volume 7, Number 8 (2014), 1851-1899.
Received: 16 January 2014
Revised: 5 July 2014
Accepted: 11 August 2014
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28A51: Lifting theory [See also 46G15] 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 70S15: Yang-Mills and other gauge theories 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]
Petrache, Mircea; Rivière, Tristan. Global gauges and global extensions in optimal spaces. Anal. PDE 7 (2014), no. 8, 1851--1899. doi:10.2140/apde.2014.7.1851. https://projecteuclid.org/euclid.apde/1513731627