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2014 Global gauges and global extensions in optimal spaces
Mircea Petrache, Tristan Rivière
Anal. PDE 7(8): 1851-1899 (2014). DOI: 10.2140/apde.2014.7.1851

Abstract

We consider the problem of extending functions ϕ:SnSn to functions u:Bn+1Sn for n=2,3. We assume ϕ belongs to the critical space W1,n and we construct a W1,(n+1,)-controlled extension u. The Lorentz–Sobolev space W1,(n+1,) is optimal for such controlled extension. Then we use these results to construct global controlled gauges for L4-connections over trivial SU(2)-bundles in 4 dimensions. This result is a global version of the local Sobolev control of connections obtained by K. Uhlenbeck.

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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

Information

Received: 16 January 2014; Revised: 5 July 2014; Accepted: 11 August 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1328.46034
MathSciNet: MR3318742
Digital Object Identifier: 10.2140/apde.2014.7.1851

Subjects:
Primary: 28A51 , 46E35
Secondary: 58J05 , 70S15

Keywords: conformally invariant problem , global gauge , Hopf lift , Lorentz spaces , nonlinear extension , nonlinear Sobolev space , Yang–Mills

Rights: Copyright © 2014 Mathematical Sciences Publishers

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