Decay estimates for Rivi\`ere's equation, with applications to regularity and compactness

Ben Sharp; Peter Topping

Decay estimates for Rivi\`ere's equation, with applications to regularity and compactness

Analysis of PDEs 2011-04-04 v2 Differential Geometry

Authors: Ben Sharp , Peter Topping

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 Rivi\`ere. 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.

Cite

@article{arxiv.1102.0713,
  title  = {Decay estimates for Rivi\`ere's equation, with applications to regularity and compactness},
  author = {Ben Sharp and Peter Topping},
  journal= {arXiv preprint arXiv:1102.0713},
  year   = {2011}
}

Comments

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

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