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An $ L^p$ regularity theory for harmonic maps


Author: Roger Moser
Journal: Trans. Amer. Math. Soc. 367 (2015), 1-30
MSC (2010): Primary 53C44, 58E20; Secondary 35B65
DOI: https://doi.org/10.1090/S0002-9947-2014-06282-X
Published electronically: May 20, 2014
MathSciNet review: 3271251
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Abstract: Motivated by the harmonic map heat flow, we consider maps between Riemannian manifolds such that the tension field belongs to an $ L^p$-space. Under an appropriate smallness condition, a certain degree of regularity follows. For suitable solutions of the harmonic map heat flow, we have a partial regularity result as a consequence.


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Additional Information

Roger Moser
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
Email: r.moser@bath.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-2014-06282-X
Received by editor(s): April 23, 2012
Published electronically: May 20, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.