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Advances in Calculus of Variations

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Estimates for the energy density of critical points of a class of conformally invariant variational problems

Tobias Lamm
  • Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 10, 60054 Frankfurt, Germany
  • Email:
/ Longzhi Lin
  • Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA
  • Email:
Published Online: 2012-07-20 | DOI: https://doi.org/10.1515/acv-2012-0104

Abstract.

We show that the energy density of critical points of a class of conformally invariant variational problems with small energy on the unit 2-disk lies in the local Hardy space . As a corollary we obtain a new proof of the energy convexity and uniqueness result for weakly harmonic maps with small energy on B1.

Keywords: Conformally invariant variational problems; energy density; local Hardy space; weakly harmonic maps

About the article

Received: 2012-02-20

Revised: 2012-06-12

Accepted: 2012-06-25

Published Online: 2012-07-20

Published in Print: 2013-10-01



Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0104. Export Citation

Citing Articles

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[1]
Tobias Lamm and Ben Sharp
Communications in Partial Differential Equations, 2015
[2]
Longzhi Lin
Analysis & PDE, 2013, Volume 6, Number 8, Page 1899

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