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Transactions of the American Mathematical Society

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Decay estimates for Rivière's equation, with applications to regularity and compactness


Authors: Ben Sharp and Peter Topping
Journal: Trans. Amer. Math. Soc. 365 (2013), 2317-2339
MSC (2010): Primary 42B37, 35A23, 35B65
Published electronically: December 12, 2012
MathSciNet review: 3020100
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Abstract: We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in $ \mathbb{R}^2$ introduced by Rivière. Applications include sharp regularity results and compactness theorems which generalise a large amount of previous geometric PDE theory, including some of the theory of harmonic and almost-harmonic maps from surfaces.


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Additional Information

Ben Sharp
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Address at time of publication: Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

Peter Topping
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05671-6
Received by editor(s): April 1, 2011
Published electronically: December 12, 2012
Article copyright: © Copyright 2012 the authors