Decay estimates for Rivière’s equation, with applications to regularity and compactness
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- by Ben Sharp and Peter Topping PDF
- Trans. Amer. Math. Soc. 365 (2013), 2317-2339
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.References
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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
- MR Author ID: 1008414
- Peter Topping
- Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
- MR Author ID: 624162
- ORCID: 0000-0002-7346-7643
- Received by editor(s): April 1, 2011
- Published electronically: December 12, 2012
- © Copyright 2012 the authors
- Journal: Trans. Amer. Math. Soc. 365 (2013), 2317-2339
- MSC (2010): Primary 42B37, 35A23, 35B65
- DOI: https://doi.org/10.1090/S0002-9947-2012-05671-6
- MathSciNet review: 3020100