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2014 Angular energy quantization for linear elliptic systems with antisymmetric potentials and applications
Paul Laurain, Tristan Rivière
Anal. PDE 7(1): 1-41 (2014). DOI: 10.2140/apde.2014.7.1

Abstract

We establish a quantization result for the angular part of the energy of solutions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimensions. This quantization is a consequence of uniform Lorentz–Wente type estimates in degenerating annuli. Moreover this result is optimal in the sense that we exhibit a sequence of functions satisfying our hypothesis whose radial part of the energy is not quantized. We derive from this angular quantization the full energy quantization for general critical points to functionals which are conformally invariant or also for pseudoholomorphic curves on degenerating Riemann surfaces.

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Paul Laurain. Tristan Rivière. "Angular energy quantization for linear elliptic systems with antisymmetric potentials and applications." Anal. PDE 7 (1) 1 - 41, 2014. https://doi.org/10.2140/apde.2014.7.1

Information

Received: 1 December 2011; Revised: 7 February 2013; Accepted: 3 April 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1295.35204
MathSciNet: MR3219498
Digital Object Identifier: 10.2140/apde.2014.7.1

Subjects:
Primary: 35J20 , 35J47 , 35J60 , 53C42 , 58E20
Secondary: 32Q65 , 49Q05 , 53C21

Keywords: analysis of PDEs , Differential geometry

Rights: Copyright © 2014 Mathematical Sciences Publishers

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