Title of article :
Gamma limit of the nonself-dual Chern–Simons–Higgs
energy
Author/Authors :
Matthias Kurzke، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Abstract :
We consider the Gamma limit of the Abelian Chern–Simons–Higgs energy
Gcsh :=
1
2 U
|∇Aεuε|2 +
μ2
4
|curlAε − hex|2
|uε|2 +
1
ε2 |uε|2 1 − |uε|2 2
dx
on a bounded, simply connected, two-dimensional domain under the ε→0 limit. As a first step we study
the Gamma limit of
Ecsh :=
1
2 U
|∇uε|2 +
1
ε2 |uε|2 1 − |uε|2 2
dx
under two different scalings; Ecsh ≈ |log ε| and Ecsh ≈ |log ε|2. We apply the |log ε|2-scaling result to the
full Chern–Simons–Higgs energy Gcsh, and as a consequence we are able to compute the first critical field
H1 = H1(U,μ) for the nucleation of a vortex. The method entails estimating in certain weak topologies the
Jacobian J(uε) = det(∇uε) in terms of the Chern–Simons–Higgs energy Ecsh.
© 2008 Elsevier Inc. All rights reserved.
Keywords :
Chern–Simons–Higgs theory , gamma convergence , Jacobian compactness , Vortices , Critical field
Journal title :
Journal of Functional Analysis
Journal title :
Journal of Functional Analysis