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

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

2009-11-22

arxiv.org/abs/0911.4224v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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 $\pm 1$.

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