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This is the second in a series of papers in which we derive a $\Gamma$-expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems.
Über das isoperimetrische Defizit ebener Figuren
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A property of Sobolev spaces
H. Brézis and F. Browder · 1979
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Effect of cross-links on a mixture of polymers
P. G. de Gennes · 1979
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Bonnesen-style isoperimetric inequalities
R. Osserman · 1979
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Theory of inhomogeneous electron gas
S. Lundqvist and N. H. March, editors · 1983
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F. H. Stillinger · 1983
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T. Ohta and K. Kawasaki · 1986
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S. Müller · 1993
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F. Bethuel, H. Brézis, F. Hélein. Ginzburg-Landau Vortices
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Microdomain structures in polyelectrolyte systems: calculation of the phase diagrams by direct minimization of the free energy
I. A. Nyrkova, A. R. Khokhlov, and M. Doi · 1994
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Reaction-controlled morphology of phase-separating mixtures
S. Glotzer, E. A. Di Marzio, and M. Muthukumar · 1995
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M. Tinkham. Introduction to superconductivity. Second edition
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Theory of domain patterns in systems with long-range interactions of Coulombic type
C. B. Muratov · 1998
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J. Funct. Anal., 152:379–403, 1998
E. Sandier. Lower bounds for the energy of unit vector fields and applications, · 1998
Cited alongside, same era.
SIAM J. Math. Anal
R. Jerrard. Lower bounds for generalized Ginzburg-Landau functionals · 1999
Cited alongside, same era.
Mathematical Aspects of Microphase Separation in Diblock Copolymers
R. Choksi · 2000
Cited alongside, same era.
Finite scale microstructures in nonlocal elasticity
X. Ren and L. Truskinovsky · 2000
Cited alongside, same era.
Ann. Sci. de l’ENS,
E. Sandier, S. Serfaty. A rigorous derivation of a free boundary problem arising in superconductivity, · 2000
Cited alongside, same era.
Connected components of sets of finite perimeter with applications to image processing
L. Ambrosio, V. Caselles, S. Masnou, and J.M Morel · 2001
Cited alongside, same era.
Asymptotic expansions by Γ \Gamma -convergence
A. Braides and L. Truskinovsky · 2008
Later among the works it cites.
The sharp quantitative isoperimetric inequality
N. Fusco, F. Maggi, and A. Pratelli · 2008
Later among the works it cites.
SIAM Journal of Applied Mathematics,
R. Choksi, M. Peletier, J. F. Williams. On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional · 2009
Later among the works it cites.
Uniform energy and density distribution: diblock copolymers’ functional
E. Spadaro · 2009
Later among the works it cites.
Uniform Energy Distribution for an Isoperimetric Problem With Long-range Interactions
G. Alberti, R. Choksi, F. Otto · 2010
Later among the works it cites.
Small volume fraction limit of the diblock copolymer problem: I. Sharp interface functional
R. Choksi and M. A. Peletier · 2010
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Analysis
E. H. Lieb and M. Loss · 2001
Cited alongside, same era.
A. Braides. Gamma-Convergence for Beginners
2002
Cited alongside, same era.
Theory of domain patterns in systems with long-range interactions of Coulomb type
C. B. Muratov · 2002
Cited alongside, same era.
Structure of stable solutions of a one-dimensional variational problem
N. K. Yip · 2006
Cited alongside, same era.
X. Chen, Y. Oshita. An Application of the Modular Function in Nonlocal Variational Problems, Arch. Rational Mech. Anal
2007
Cited alongside, same era.
E. Sandier, S. Serfaty. Vortices in the Magnetic Ginzburg-Landau Model
2007
Cited alongside, same era.
Later among the works it cites.
Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions
C. B. Muratov · 2010
Later among the works it cites.
A note on the global minimizers of the nonlocal isoperimetric problem in two dimensions
P. Sternberg and I. Topaloglu · 2010
Later among the works it cites.
Small volume fraction limit of the diblock copolymer problem: II. Diffuse interface functional
R. Choksi and M. A. Peletier · 2011
Later among the works it cites.
E. Sandier, S. Serfaty. Improved Lower Bounds for Ginzburg-Landau Energies via Mass Displacement, Analysis & PDE, 4-5:757–795, 2011
2011
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A note on linear elliptic systems on ℝ d \mathbb{R}^{d}
C. Ortner and E. Süli · 2012
Closest in time.
E. Sandier, S. Serfaty. From Ginzburg Landau to Vortex Lattice Problems, Comm. Math. Phys
2012
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