A zigzag pattern in micromagnetics

Alouges, 2002, Néel and cross-tie wall energies for planar micromagnetic configurations, ESAIM Control Optim. Calc. Var., 8, 31, 10.1051/cocv:2002017 Ambrosio, 1990, A general chain rule for distributional derivatives, Proc. Amer. Math. Soc., 108, 691, 10.1090/S0002-9939-1990-0969514-3 Ambrosio, 1999, Line energies for gradient vector fields in the plane, Calc. Var. Partial Differential Equations, 9, 327, 10.1007/s005260050144 André, 1999, On nematics stabilized by a large external field, Rev. Math. Phys., 11, 653, 10.1142/S0129055X99000234 Aviles, 1987, A mathematical problem related to the physical theory of liquid crystal configurations, vol. 12, 1 Aviles, 1999, On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg–Landau type energy for gradient fields, Proc. Roy. Soc. Edinburgh Sect. A, 129, 1, 10.1017/S0308210500027438 Baldo, 1990, Minimal interface criterion for phase transitions in mixtures of Cahn–Hilliard fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7, 67, 10.1016/S0294-1449(16)30304-3 Bethuel, 1994, Ginzburg–Landau Vortices, vol. 13 Bethuel, 1988, Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal., 80, 60, 10.1016/0022-1236(88)90065-1 Brezis, 1995, Degree theory and BMO. I. Compact manifolds without boundaries, Selecta Math. (N.S.), 1, 197, 10.1007/BF01671566 Conti, 2007, Sharp upper bounds for a variational problem with singular perturbation, Math. Ann., 338, 119, 10.1007/s00208-006-0070-2 Conti, 2002, A Γ-convergence result for the two-gradient theory of phase transitions, Comm. Pure Appl. Math., 55, 857, 10.1002/cpa.10035 Dávila, 2003, Lifting of BV functions with values in S1, C. R. Math. Acad. Sci. Paris, 337, 159, 10.1016/S1631-073X(03)00314-5 De Lellis, 2003, Structure of entropy solutions to the eikonal equation, J. Eur. Math. Soc. (JEMS), 5, 107, 10.1007/s10097-002-0048-7 DeSimone, 2000, Magnetic microstructures—a paradigm of multiscale problems, 175 DeSimone, 2001, A compactness result in the gradient theory of phase transitions, Proc. Roy. Soc. Edinburgh Sect. A, 131, 833, 10.1017/S030821050000113X DeSimone, 2003, Repulsive interaction of Néel walls, and the internal length scale of the cross-tie wall, Multiscale Model. Simul., 1, 57, 10.1137/S1540345902402734 DeSimone, 2006, Recent analytical developments in micromagnetics, 269 Fonseca, 2005, Coupled singular perturbations for phase transitions, Asymptot. Anal., 44, 299 Hang, 2001, Static theory for planar ferromagnets and antiferromagnets, Acta Math. Sin. (Engl. Ser.), 17, 541, 10.1007/s101140100136 Hubert, 1998 Ignat, 2005, The space BV(S2,S1): minimal connection and optimal lifting, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22, 283, 10.1016/j.anihpc.2004.07.003 Ignat, 2010, Vortex energy and 360° Néel walls in thin-film micromagnetics, Comm. Pure Appl. Math., 63, 1677, 10.1002/cpa.20322 Ignat, 2011, Lower bound for the energy of Bloch walls in micromagnetics, Arch. Ration. Mech. Anal., 199, 369, 10.1007/s00205-010-0325-7 Ignat, 2008, A compactness result in thin-film micromagnetics and the optimality of the Néel wall, J. Eur. Math. Soc. (JEMS), 10, 909, 10.4171/JEMS/135 Ignat, 2011, A compactness result for Landau state in thin-film micromagnetics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28, 247, 10.1016/j.anihpc.2011.01.001 Jabin, 2002, Line-energy Ginzburg–Landau models: zero-energy states, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 1, 187 Jin, 2000, Singular perturbation and the energy of folds, J. Nonlinear Sci., 10, 355, 10.1007/s003329910014 Kružík, 2006, Recent developments in the modeling, analysis, and numerics of ferromagnetism, SIAM Rev., 48, 439, 10.1137/S0036144504446187 Modica, 1987, The gradient theory of phase transitions and the minimal interface criterion, Arch. Ration. Mech. Anal., 98, 123, 10.1007/BF00251230 Modica, 1977, Un esempio di Γ−-convergenza, Boll. Unione Mat. Ital. B (5), 14, 285 Moser, 2009, On the energy of domain walls in ferromagnetism, Interfaces Free Bound., 11, 399, 10.4171/IFB/216 Poliakovsky, 2007, Upper bounds for singular perturbation problems involving gradient fields, J. Eur. Math. Soc. (JEMS), 9, 1, 10.4171/JEMS/70 Rivière, 2001, Limiting domain wall energy for a problem related to micromagnetics, Comm. Pure Appl. Math., 54, 294, 10.1002/1097-0312(200103)54:3<294::AID-CPA2>3.0.CO;2-S Rivière, 2003, Compactness, kinetic formulation, and entropies for a problem related to micromagnetics, Comm. Partial Differential Equations, 28, 249, 10.1081/PDE-120019381 E. Sandier, Asymptotics for a nematic in an electric field, preprint, Université de Tours, 1999. Schoen, 1983, Boundary regularity and the Dirichlet problem for harmonic maps, J. Diff. Geom., 18, 253, 10.4310/jdg/1214437663