CALCULUS OF VARIATION WITH APPLICATION TO GINZBURG-LANDAU THEORY
Ginzburg-Landau model was suggested in the 1950s as a phenomenological description of superconductivity. The discovery of patterns of vortices (or defects) in superconductors led to the 2003 Nobel Prize in Physics, awarded to Ginzburg, Abrikosov and Leggett. In my works, I study the existence of minimizers of Ginzburg-Landau energy in certain functional classes, as well as the structure of these minimizers.
Necessary Vonditions for the Existence of Local Ginzburg-Landau Minimizers with Prescribed Degrees on the Boundary, Asymptotic Analysis 89, 37-61, 2014.
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Minimizers of the Magnetic Ginzburg-Landau Functional in Simply Connected Domain with Prescribed Degree on the Boundary, with L. Berlyand and V. Rybalko. Communications in Contemporary Mathematics 13, 53-66, 2011.
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Ginzburg-Landau Model with Small Pinning Domains, with M. Dos Santos. Networks and Heterogeneous Media 6, 715-753, 2011.
The Ginzburg-Landau Functional with a Discontinuous and Rapidly Oscillating Pinning Term. Part I: the Zero Degree Case, with P. Mironescu and M. Dos Santos. Communications in Contemporary Mathematics 13, 885-914, 2011.
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Near Boundary Vortices in a Magnetic Ginzburg-Landau model: Their Locations via Tight Lower Bounds, with L. Berlyand and V. Rybalko. Journal of Functional Analysis 258, 1728-1762, 2010.
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PHD Thesis, 2012
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