Calculus of Variations and Partial Differential Equations

, Volume 41, Issue 1, pp 45–69

A new approximation of relaxed energies for harmonic maps and the Faddeev model


DOI: 10.1007/s00526-010-0353-z

Cite this article as:
Giaquinta, M., Hong, MC. & Yin, H. Calc. Var. (2011) 41: 45. doi:10.1007/s00526-010-0353-z


We propose a new approximation for the relaxed energy E of the Dirichlet energy and prove that the minimizers of the approximating functionals converge to a minimizer u of the relaxed energy, and that u is partially regular without using the concept of Cartesian currents. We also use the same approximation method to study the variational problem of the relaxed energy for the Faddeev model and prove the existence of minimizers for the relaxed energy \({\tilde{E}_F}\) in the class of maps with Hopf degree ±1.

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Department of MathematicsThe University of QueenslandBrisbaneAustralia
  3. 3.Department of MathematicsShanghai Jiaotong UniversityShanghaiChina