A compactness result in the gradient theory of phase transitions
From MaRDI portal
Publication:2764656
DOI10.1017/S030821050000113XzbMath0986.49009OpenAlexW2095409038WikidataQ59202368 ScholiaQ59202368MaRDI QIDQ2764656
Felix Otto, Robert V. Kohn, Antonio De Simone, Stefan Müller
Publication date: 9 April 2002
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s030821050000113x
entropyphase transitionsintegral functionalYoung measurecompensated compactnesseikonal equationsingularly perturbed variational problem
Energy minimization in equilibrium problems in solid mechanics (74G65) Variational methods applied to problems in fluid mechanics (76M30) Methods involving semicontinuity and convergence; relaxation (49J45) Phase transformations in solids (74N99)
Related Items (56)
A sharp-interface limit for a two-well problem in geometrically linear elasticity ⋮ A reduced theory for thin-film micromagnetics ⋮ The Dirichlet-to-Neumann map, viscosity solutions to eikonal equations, and the self-dual equations of pattern formation ⋮ Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 -- March 6, 2021 (hybrid meeting) ⋮ A Regularizing Property of the 2D-Eikonal Equation ⋮ Compactness, Kinetic Formulation, and Entropies for a Problem Related to Micromagnetics ⋮ Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactness ⋮ A simple proof of the characterization of functions of low Aviles Giga energy on a ballviaregularity ⋮ The rectifiability of the entropy defect measure for Burgers equation ⋮ Variational analysis of the \(J_1-J_2-J_3\) model: a non-linear lattice version of the Aviles-Giga functional ⋮ On the regularity of weak solutions to Burgers' equation with finite entropy production ⋮ Upper bounds for singular perturbation problems involving gradient fields ⋮ Rational string topology ⋮ Convergence of a ferromagnetic film model ⋮ \(\Gamma\)-limit for two-dimensional charged magnetic Zigzag domain walls ⋮ On \(\Gamma\)-convergence of a variational model for Lithium-ion batteries ⋮ Sharp upper bounds for a variational problem with singular perturbation ⋮ An SBV relaxation of the cross-Newell energy for modeling stripe patterns and their defects ⋮ Continuity Equation and Characteristic Flow for Scalar Hencky Plasticity ⋮ Factorization for entropy production of the Eikonal equation and regularity ⋮ A smectic liquid crystal model in the periodic setting ⋮ Two-dimensional unit-length vector fields of vanishing divergence ⋮ COMPACTNESS AND STRUCTURE OF ZERO-STATES FOR UNORIENTED AVILES–GIGA FUNCTIONALS ⋮ Calculus of variations. Abstracts from the workshop held August 14--20, 2022 ⋮ Regularity of the Eikonal equation with two vanishing entropies ⋮ Entropy method for line-energies ⋮ Global description of patterns far from onset: a case study ⋮ The rectifiability of entropy measures in one space dimension. ⋮ A zigzag pattern in micromagnetics ⋮ A Ginzburg--Landau-Type Problem for Highly Anisotropic Nematic Liquid Crystals ⋮ Existence of partially regular weak solutions to Landau-Lifshitz-Maxwell equations ⋮ A general technique to prove upper bounds for singular perturbation problems ⋮ A model problem for nematic-isotropic transitions with highly disparate elastic constants ⋮ A compactness result in thin-film micromagnetics and the optimality of the Néel wall ⋮ A necessary condition for lower semicontinuity of line energies ⋮ Kinetic formulation of vortex vector fields ⋮ Limiting properties of the second order Ginzburg-Landau minimizers ⋮ On scalar metrics that maximize geodesic distances in the plane ⋮ A method for establishing upper bounds for singular perturbation problems ⋮ Grain boundary motion arising from the gradient flow of the Aviles-Giga functional ⋮ Bounds on the energy of a soft cubic ferromagnet with large magnetostriction ⋮ Lower bound for the energy of Bloch walls in micromagnetics ⋮ An example in the gradient theory of phase transitions ⋮ Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations ⋮ A viscosity property of minimizing micromagnetic configurations ⋮ A variational theory for point defects in patterns ⋮ Compactness and sharp lower bound for a 2D smectics model ⋮ Homogenization of micromagnetics large bodies ⋮ Unnamed Item ⋮ Characterization of minimizers of Aviles-Giga functionals in special domains ⋮ A \(\Gamma \)-convergence result for Néel walls in micromagnetics ⋮ Rigidity of a non-elliptic differential inclusion related to the Aviles-giga conjecture ⋮ The characterization of Riemannian metric arising from phase transition problems ⋮ Limiting behavior of the Ginzburg-Landau functional ⋮ On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds ⋮ Self-similar folding patterns and energy scaling in compressed elastic sheets
This page was built for publication: A compactness result in the gradient theory of phase transitions
