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

Ben Sharp; Peter Topping

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arXiv · 1102.0713

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

Ben Sharp·Peter Topping

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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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Ben Sharp, Peter Topping. 2011-04-01. Decay estimates for Rivière's equation, with applications to regularity and compactness. https://arxiv.org/abs/1102.0713

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