Entropy method for line-energies

DOI10.1007/s00526-011-0438-3zbMath1241.49010OpenAlexW2047680238MaRDI QIDQ425161

Benoît Merlet, Radu Ignat

Publication date: 7 June 2012

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-011-0438-3

zbMATH Keywords

viscosity solutionenergy functionalslower semicontinuous line-energiesthin-film micromagneticswall-energies

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Harmonic maps, etc. (58E20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Statistical mechanics of magnetic materials (82D40)

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Cites Work

• Unnamed Item
• Unnamed Item
• A compactness result for Landau state in thin-film micromagnetics
• Lower bound for the energy of Bloch walls in micromagnetics
• Two remarks on liftings of maps with values into \(S^1\).
• Upper bounds for singular perturbation problems involving gradient fields
• Sharp upper bounds for a variational problem with singular perturbation
• The morphology and folding patterns of buckling-driven thin-film blisters
• Structure of entropy solutions to the eikonal equation
• Lifting of BV functions with values in \(S^1\)
• Singular perturbation and the energy of folds
• Line energies for gradient vector fields in the plane
• The space \(\operatorname{BV}(S^2,S^1)\): minimal connection and optimal lifting
• A compactness result in the gradient theory of phase transitions
• Vortex energy and 360° Néel walls in thin-film micromagnetics
• On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg–Landau type energy for gradient fields
• An example in the gradient theory of phase transitions
• Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations
• The distance function and defect energy
• Magnetic clusters and fold energies