Leonid Berlyand, Mathematics and Materials Research Institute, Penn State University
"Ginzburg-Landau minimizers with prescribed degrees Capacity of the domain and emergence of vortices"
Let be a 2D domain with holes . In domain consider class of complex valued maps having degrees and on , respectively and degree on .
We show that if cap, minimizers of the Ginzburg-Landau energy exist for each . They are vortexless and converge in to a minimizing -valued harmonic map as the coherency length tends to . When cap, we establish existence of quasi-minimizers, which exhibit a different qualitative behavior: they have exactly two zeroes (vortices) rapidly converging to .
This is a joint work with P. Mironescu (Orsay, France).
TUESDAY, May 3, 2005