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Steklov problems in perforated domains with a coefficient of indefinite sign
Renormalized Ginzburg-Landau energy and location of near boundary vortices
1. | Department of Mathematics, Penn State University, University Park, State College, PA 16802, United States |
2. | Mathematical Division, B. I. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, Kharkov 61103, Ukraine |
3. | Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907 |
References:
[1] |
N. André and I. Shafrir, On the minimizers of a Ginzburg-Landau-type energy when the boundary condition has zeros, Adv. Differential Equations, 9 (2004), 891-960. |
[2] |
P. Bauman, N. N. Carlson and D. Phillips, On the zeros of solutions to Ginzburg-Landau type systems, SIAM J. Math. Anal., 24 (1993), 1283-1293.
doi: 10.1137/0524073. |
[3] |
F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calculus of Variations and PDEs, 1 (1993), 123-148.
doi: 10.1007/BF01191614. |
[4] |
F. Bethuel, H. Brezis and F. Hélein, "Ginzburg-Landau Vortices," Progress in Nonlinear Differential Equations and their Applications, 13, Birkhäuser Boston, Inc., Boston, MA, 1994. |
[5] |
A. Boutet de Monvel-Berthier, V. Georgescu and R. Purice, A boundary value problem related to the Ginzburg-Landau model, Comm. Math. Phys., 142 (1991), 1-23.
doi: 10.1007/BF02099170. |
[6] |
L. Berlyand and P. Mironescu, Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices, J. Funct. Anal., 239 (2006), 76-99.
doi: 10.1016/j.jfa.2006.03.006. |
[7] |
L. Berlyand and V. Rybalko, Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation, J. Eur. Math. Soc., 12 (2010), 1497-1531.
doi: 10.4171/JEMS/239. |
[8] |
L. Berlyand and K. Voss, Symmetry breaking in annular domains for a Ginzburg-Landau superconductivity model, in "Proceedings of IUTAM 99/4 Symposium," Sydney, Australia, Kluwer Acad. Publ., (2001), 189-200. |
[9] |
R. L. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals, SIAM J. Math. Anal., 30 (1999), 721-746.
doi: 10.1137/S0036141097300581. |
[10] |
M. Kurzke, Boundary vortices in thin magnetic films, Calc. Var. Partial Differential Equations, 26 (2006), 1-28. |
[11] |
P. Mironescu, Explicit bounds for solutions to a Ginzburg-Landau type equations, Rev. Roumain Math. Pure Appl., 41 (1996), 263-271. |
[12] |
W.-M. Ni and I. Takagi, Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J., 70 (1993), 247-281. |
[13] |
B. White, Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math., 160 (1988), 1-17.
doi: 10.1007/BF02392271. |
show all references
References:
[1] |
N. André and I. Shafrir, On the minimizers of a Ginzburg-Landau-type energy when the boundary condition has zeros, Adv. Differential Equations, 9 (2004), 891-960. |
[2] |
P. Bauman, N. N. Carlson and D. Phillips, On the zeros of solutions to Ginzburg-Landau type systems, SIAM J. Math. Anal., 24 (1993), 1283-1293.
doi: 10.1137/0524073. |
[3] |
F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calculus of Variations and PDEs, 1 (1993), 123-148.
doi: 10.1007/BF01191614. |
[4] |
F. Bethuel, H. Brezis and F. Hélein, "Ginzburg-Landau Vortices," Progress in Nonlinear Differential Equations and their Applications, 13, Birkhäuser Boston, Inc., Boston, MA, 1994. |
[5] |
A. Boutet de Monvel-Berthier, V. Georgescu and R. Purice, A boundary value problem related to the Ginzburg-Landau model, Comm. Math. Phys., 142 (1991), 1-23.
doi: 10.1007/BF02099170. |
[6] |
L. Berlyand and P. Mironescu, Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices, J. Funct. Anal., 239 (2006), 76-99.
doi: 10.1016/j.jfa.2006.03.006. |
[7] |
L. Berlyand and V. Rybalko, Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation, J. Eur. Math. Soc., 12 (2010), 1497-1531.
doi: 10.4171/JEMS/239. |
[8] |
L. Berlyand and K. Voss, Symmetry breaking in annular domains for a Ginzburg-Landau superconductivity model, in "Proceedings of IUTAM 99/4 Symposium," Sydney, Australia, Kluwer Acad. Publ., (2001), 189-200. |
[9] |
R. L. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals, SIAM J. Math. Anal., 30 (1999), 721-746.
doi: 10.1137/S0036141097300581. |
[10] |
M. Kurzke, Boundary vortices in thin magnetic films, Calc. Var. Partial Differential Equations, 26 (2006), 1-28. |
[11] |
P. Mironescu, Explicit bounds for solutions to a Ginzburg-Landau type equations, Rev. Roumain Math. Pure Appl., 41 (1996), 263-271. |
[12] |
W.-M. Ni and I. Takagi, Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J., 70 (1993), 247-281. |
[13] |
B. White, Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math., 160 (1988), 1-17.
doi: 10.1007/BF02392271. |
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