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

1102.0713Feb 3, 201126 pages, updated bibliographic information and discussion of examples showing that the results are sharp

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

Ben Sharp, Peter Topping

Analysis of PDEs Differential Geometry

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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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We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in R² 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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The paper addresses: Decay estimates for Rivière's equation, with applications to regularity and compactness.
We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in R² introduced by Rivière.

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Author comment: 26 pages, updated bibliographic information and discussion of examples showing that the results are sharp