On periodic critical points and local minimizers of the Ohta-Kawasaki functional

DOI10.1016/j.na.2017.11.004zbMath1385.49025arXiv1511.04956OpenAlexW2963108971MaRDI QIDQ681974

Riccardo Cristoferi

Publication date: 13 February 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04956

zbMATH Keywords

second variationlocal minimizersnonlocal isoperimetric problemOhta-Kawasaki energyperiodic critical points

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Methods involving semicontinuity and convergence; relaxation (49J45) Periodic optimal control problems (49N20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Minimality via second variation for a nonlocal isoperimetric problem
• On the global minimizers of a nonlocal isoperimetric problem in two dimensions
• Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems
• Uniform energy and density distribution: diblock copolymers' functional
• Singular perturbations as a selection criterion for periodic minimizing sequences
• On energy minimizers of the diblock copolymer problem
• On the derivation of a density functional theory for microphase separation of diblock copolymers
• A selection principle for the sharp quantitative isoperimetric inequality
• On a nonlocal isoperimetric problem on the two-sphere
• The sharp quantitative isoperimetric inequality
• Minimality via second variation for microphase separation of diblock copolymer melts
• Stability in shape optimization with second variation
• The \(\Gamma\)-limit of the two-dimensional Ohta-Kawasaki energy. Droplet arrangement via the renormalized energy
• The \(\varGamma\)-limit of the two-dimensional Ohta-Kawasaki energy. I: Droplet density
• Droplet Minimizers of an Isoperimetric Problem with Long-Range Interactions
• Cascade of Minimizers for a Nonlocal Isoperimetric Problem in Thin Domains
• Stability of spot and ring solutions of the diblock copolymer equation
• Uniform energy distribution for an isoperimetric problem with long-range interactions
• Small Volume-Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional
• MANY DROPLET PATTERN IN THE CYLINDRICAL PHASE OF DIBLOCK COPOLYMER MORPHOLOGY
• Spherical Solutions to a Nonlocal Free Boundary Problem from Diblock Copolymer Morphology
• Local minimisers and singular perturbations
• A strong minimax property of nondegenerate minimal submanifolds.
• Concentrically layered energy equilibria of the di-block copolymer problem
• Local and global minimality results for an isoperimetric problem with long-range interactions
• Small Volume Fraction Limit of the Diblock Copolymer Problem: I. Sharp-Interface Functional
• On the first and second variations of a nonlocal isoperimetric problem
• Singular Limit Problem for Some Elliptic Systems
• Wriggled Lamellar Solutions and Their Stability in the Diblock Copolymer Problem
• Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions