## Leonid Berlyand, Mathematics and Materials Research Institute, Penn State University

"Ginzburg-Landau minimizers with prescribed degrees Capacity of the domain and emergence of vortices"

#### Abstract

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
Time: 1:30 P.M.
Location: DH 4303