Decay estimates for Rivière’s equation, with applications to regularity and compactness. (English) Zbl 1270.35152
Summary: 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.
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 35J47 | Second-order elliptic systems |
| 42B37 | Harmonic analysis and PDEs |
| 35A23 | Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
energy estimatesReferences:
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