Talk

The Jacobian and the Ginzburg-Landau energy

  • Robert Jerrard (Urbana/Champaign + MPI MiS, Leipzig)
A3 01 (Sophus-Lie room)

Abstract

We show that if the Ginzburg-Landau energy Iϵ(uϵ):=1|lnϵ|Ω12|uϵ|2+(1|uϵ|2)24ϵ2   uϵ:RmΩR2   m2 is uniformly bounded for a sequence of functions uϵ as ϵ0, then the Jacobians {Juϵ} are precompact in a ppropriate weak topologies. We further show that any limiting measure must be rectifiable. These results have potential applications in problems a variety of problems, including for example questions involving dynamics of vortex filaments in superfluids. (joint work with Mete Soner)

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