Communications on Pure and Applied Mathematics · 2002 · 68 citations · 27 references
Natural SciencesMathematicsComputational ThermodynamicsCondensed Matter PhysicsPhysical ChemistryCritical PhenomenaDissipative SystemsPerturbation TheoryPhase EquilibriaPhase TransitionsSingular Perturbation TheoryGradient Energy TheoryInterfacial Free EnergyNon-degenerate Perturbation TheorySingular Perturbation AnalysisSingular Perturbations In Partial Differential Equations
Abstract The generalization to gradient vector fields of the classical double‐well, singularly perturbed functionals, where W (ξ) = 0 if and only if ξ = A or ξ = B , and A − B is a rank‐1 matrix, is considered. Under suitable constitutive and growth hypotheses on W , it is shown that I ε Γ‐converge to where K * is the (constant) interfacial energy per unit area. © 2002 Wiley Periodicals, Inc.
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Ronald Gariepy · Bulletin of the London Mathematical Society · 2001 · 1.3K citations
Engineering, Mechanical Engineering, Finite Element Analysis +6