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References (40)
-
V. Ennola (1964)
A remark about the Epstein zeta functionProc. Glasg. Math. Assoc., 6
-
J.W.S. Cassels (1959)
On a problem of Rankin about the Epstein zeta-functionProc. Glasgow Math. Assoc., 4
-
N.M. Rivière (1971)
Singular integrals and multiplier operatorsArk. Mat., 9
-
E. Sandier, S. Serfaty (2011)
Improved Lower Bounds for Ginzburg-Landau Energies via Mass DisplacementAnalysis and PDE, 4-5
-
M. Struwe (1994)
On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensionsDiff. and Int. Eqs., 7
-
X. Chen, Y. Oshita (2007)
An application of the modular function in nonlocal variational problemsArch. Rat. Mech. Anal., 186
-
S. Fournais, B. Helffer (2006)
On the third critical field in Ginzburg-Landau theoryComm. Math. Phys., 266
-
E. Sandier (1998)
Lower bounds for the energy of unit vector fields and applicationsJ. Funct. Anal., 152
-
H. Aydi, E. Sandier (2009)
Vortex analysis of the periodic Ginzburg-Landau modelAnn. Inst. H. Poincaré Anal. Non Linéaire, 26
-
P. Billingsley (1999)
Convergence of probability measures -
R. M. Hervé, M. Hervé (1994)
Étude qualitative des solutions réelles d’une équation différentielle liée à l’équation de Ginzburg-LandauAnn. Inst. H. Poincaré Anal. Non Linéaire, 11
-
N. Korevaar, J.L. Lewis (1987)
Convex solutions of certain elliptic equations have constant rank HessiansArch. Rat. Mech. Anal., 97
-
H.L. Montgomery (1988)
Minimal Theta functionsGlasgow Math J., 30
-
J. Frehse (1972)
On the regularity of the solution of a second order variational inequalityBoll. Un. Mat. Ital. (4), 6
-
H. Brezis, D. Kinderlehrer (1973)
The smoothness of solutions to nonlinear variational inequalitiesIndiana Univ. Math. J., 23
-
P. Mironescu (1996)
Les minimiseurs locaux pour l’équation de Ginzburg-Landau sont à symétrie radialeC. R. Acad. Sci. Paris Sér. I Math., 323
-
J. Dolbeault, R. Monneau (2002)
Convexity Estimates for Nonlinear Elliptic Equations and Application to Free Boundary ProblemsAnn. Inst. H. Poincaré, Analyse Non Linéaire, 19
-
D. Kinderlehrer, L. Nirenberg (1977)
Regularity in free boundary problemsAnn. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4
-
A. Aftalion, S. Serfaty (2007)
Lowest Landau level approach in superconductivity for the Abrikosov lattice close to H c_2Selecta Math, 13
-
B. Kawohl (1985)
When are solutions to nonlinear elliptic boundary value problems convex?Comm. PDE, 10
-
L. Caffarelli (1977)
The regularity of free boundaries in higher dimensionsActa Math., 139
-
R.L. Jerrard (1999)
Lower bounds for generalized Ginzburg-Landau functionalsSIAM J. Math. Anal., 30
-
E. Sandier, S. Serfaty (2000)
Global Minimizers for the Ginzburg-Landau Functional below the First critical Magnetic FieldAnnales Inst. H. Poincaré, Anal. non linéaire, 17
-
G. Alberti, S. Müller (2001)
A new approach to variational problems with multiple scalesComm. Pure Appl. Math., 54
-
L.A. Caffarelli, A. Friedman (1985)
Convexity of solutions of semilinear elliptic equationsDuke Math. J., 52
-
R.A. Rankin (1953)
A minimum problem for the Epstein zeta functionProc. Glasgow Math. Assoc, 1
-
V. Ennola (1964)
On a problem about the Epstein zeta-functionProc. Cambridge Philos. Soc., 60
-
C. Radin (1981)
The ground state for soft disksJ. Stat. Phys., 26
-
G. Alberti, R. Choksi, F. Otto (2009)
Uniform Energy Distribution for an Isoperimetric Problem With Long-range InteractionsJ. Amer. Math. Soc., 22
-
H. Brezis (1972)
Problèmes unilatérauxJ. Math. Pures Appl. (9), 51
-
M.E. Becker (1981)
Multiparameter groups of measure-preserving transformations: a simple proof of Wiener ergodic theoremAnn. Probability, 9
-
A. Friedman, D. Phillips (1984)
The free boundary of a semilinear elliptic equationTrans. Amer. Math. Soc., 282
-
R.L. Jerrard, H.M. Soner (2002)
The Jacobian and the Ginzburg-Landau energyCalc. Var. Partial Differential Equations, 14
-
H. Brezis, S. Serfaty (2002)
A variational formulation for the two-sided obstacle problem with measure dataCommun. Contemp. Math., 4
-
V.M. Isakov (1975)
Inverse theorems on the smoothness of potentialsDifferencial’nye Uravnenija, 11
-
H. Cohn, A. Kumar (2007)
Universally optimal distribution of points on spheresJ. Amer. Math. Soc., 20
-
E. Sandier, S. Serfaty (2003)
The decrease of bulk-superconductivity close to the second critical field in the Ginzburg-Landau modelSIAM J. Math. Anal., 34
-
C. Muratov (2010)
Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensionsCommun. Math. Phys., 299
-
F. Theil (2006)
A proof of crystallization in two dimensionsCommun. Math. Phys., 262
-
P.H. Diananda (1964)
Notes on two lemmas concerning the Epstein zeta-functionProc. Glasgow Math. Assoc., 6
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Springer-Verlag
- Subject
- Physics; Classical and Quantum Gravitation, Relativity Theory; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Quantum Physics; Mathematical Physics
- ISSN
- 0010-3616
- eISSN
- 1432-0916
- DOI
- 10.1007/s00220-012-1508-x
- Publisher site
- See Article on Publisher Site
Abstract
We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general remains open.
Journal
Communications in Mathematical Physics – Springer Journals
Published: Jun 17, 2012