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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 46
  3. Calculus of Variations and Partial Differential Equations : Volume 46, Issue 3-4, March 2013
  4. Uniqueness of vortexless Ginzburg-Landau type minimizers in two dimensions
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 46, Issue 3-4, March 2013
Well-posedness for the fractional Landau–Lifshitz equation without Gilbert damping
On Ricci coefficients of null hypersurfaces with time foliation in Einstein vacuum space-time: part I
Maximum Principles for vectorial approximate minimizers of nonconvex functionals
Uniqueness of vortexless Ginzburg-Landau type minimizers in two dimensions
Random Steiner symmetrizations of sets and functions
Regularity for Dirac-harmonic map with Ricci type spinor potential
Layered solutions with multiple asymptotes for non autonomous Allen–Cahn equations in $${\mathbb {R}^{3}}$$
On the long-time behavior of some mathematical models for nematic liquid crystals
Ground states for quasilinear Schrödinger equations with critical growth
Viscosity solutions of Eikonal equations on topological networks
A variational approach to the inviscous limit of fractional conservation laws
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian
Discontinuous solutions of Hamilton–Jacobi–Bellman equation under state constraints
Isoperimetric inequalities for an ergodic stochastic control problem
Regularity results for differential forms solving degenerate elliptic systems
Infinitely many solutions for the prescribed curvature problem of polyharmonic operator
Existence and regularity results for the Steiner problem
Light reflection is nonlinear optimization
A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
Calculus of Variations and Partial Differential Equations : Volume 46, Issue 1-2, January 2013
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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Uniqueness of vortexless Ginzburg-Landau type minimizers in two dimensions

Content Provider SpringerLink
Author Farina, Alberto Mironescu, Petru
Copyright Year 2012
Abstract In a simply connected two dimensional domain Ω, we consider Ginzburg-Landau minimizers u with zero degree Dirichlet boundary condition $${g \in H^{1/2}(\partial \Omega; \mathbb{S}^1)}$$ . We prove uniqueness of u whenever either the energy or the Ginzburg-Landau parameter are small. This generalizes a result of Ye and Zhou requiring smoothness of g. We also obtain uniqueness when Ω is multiply connected and the degrees of the vortexless minimizer u are prescribed on the components of the boundary, generalizing a result of Golovaty and Berlyand for annular domains. The proofs rely on new global estimates connecting the variation of |u| to the Ginzburg-Landau energy of u. These estimates replace the usual global pointwise estimates satisfied by $${\nabla u}$$ when g is smooth, and apply to fairly general potentials. In a related direction, we establish new uniqueness results for critical points of the Ginzburg-Landau energy.
Ending Page 554
Page Count 32
Starting Page 523
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 46
Language English
Publisher Springer-Verlag
Publisher Date 2012-01-17
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Ginzburg-Landau equations Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness Degree, winding number Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Nonlinear elliptic equations Variational methods for elliptic systems
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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