On the formation of microstructure for singularly perturbed problems with two, three, or four preferred gradients

Variational inequalities (49J40) Singular perturbations in context of PDEs (35B25) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Analysis of microstructure in solids (74N15)

Cites Work

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Domain structure of bulk ferromagnetic crystals in applied fields near saturation
Deformation concentration for martensitic microstructures in the limit of low volume fraction
Energy bounds for a compressed elastic film on a substrate
Microstructures in low-hysteresis shape memory alloys: scaling regimes and optimal needle shapes
Self-similar folding patterns and energy scaling in compressed elastic sheets
Asymptotic analysis of hierarchical martensitic microstructure
Quasiconvex functions incorporating volumetric constraints are rank-one convex
Domain branching in uniaxial ferromagnets: asymptotic behavior of the energy
Domain branching in uniaxial ferromagnets: A scaling law for the minimum energy
Energy minimization and flux domain structure in the intermediate state of a type-I superconductor
Dislocation microstructures and the effective behavior of single crystals
Energy scaling of compressed elastic films -- three-dimensional elasticity and reduced theories
Convex integration with constraints and applications to phase transitions and partial differential equations
Bounds on the energy of a soft cubic ferromagnet with large magnetostriction
On the energy scaling behaviour of a singularly perturbed Tartar square
Energy scaling law for a singularly perturbed four-gradient problem in helimagnetism
Exact constructions in the (non-linear) planar theory of elasticity: from elastic crystals to nematic elastomers
Micromagnetics of Galfenol
2-D stability of the Néel wall
A lower bound for a variational model for pattern formation in shape-memory alloys
Low volume-fraction microstructures in martensites and crystal plasticity
Branched Microstructures in the Ginzburg--Landau Model of Type-I Superconductors
A quantitative rigidity result for the cubic-to-tetragonal phase transition in the geometrically linear theory with interfacial energy
Explicit Construction of Piecewise Affine Mappings with Constraints
Optimal Fine-Scale Structures in Compliance Minimization for a Shear Load
Nucleation barriers at corners for a cubic-to-tetragonal phase transformation
A rigidity result for a perturbation of the geometrically linear three‐well problem
Surface energy and microstructure in coherent phase transitions
Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc})
Nucleation Barriers for the Cubic‐to‐Tetragonal Phase Transformation
Variational Analysis of a Two-Dimensional Frustrated Spin System: Emergence and Rigidity of Chirality Transitions
Energy scaling and branched microstructures in a model for shape-memory alloys with SO(2) invariance
Emergent parabolic scaling of nano-faceting crystal growth
Wrinkles as the Result of Compressive Stresses in an Annular Thin Film
Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor
Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys
The concertina pattern. From micromagnetics to domain theory
Optimal scaling in solids undergoing ductile fracture by crazing
Energy scaling laws for microstructures: from helimagnets to martensites