Displacement Convexity and Minimal Fronts at Phase Boundaries

We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition are strictly convex in the sense of displacement convexity under a natural change of variables.We use this to show that, in certain cases, the only critical point...

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Bibliographic Details
Published inArchive for rational mechanics and analysis Vol. 194; no. 3; pp. 823 - 847
Main Authors Carlen, E. A., Carvalho, M. C., Esposito, R., Lebowitz, J. L., Marra, R.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2009
Springer
Springer Nature B.V
Subjects
Classical Mechanics
Classical statistical mechanics
Complex Systems
Exact sciences and technology
Fluid- and Aerodynamics
Kinetic theory
Mathematical and Computational Physics
Physics
Physics and Astronomy
Statistical physics, thermodynamics, and nonlinear dynamical systems
Studies
Theoretical
Lagrange Equation
Convex Structure
Single Component System
Component Case
Strict Convexity
Convexity
Domain structure
Statistical mechanics
Critical points
Variable transformation
Free energy
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Summary:We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition are strictly convex in the sense of displacement convexity under a natural change of variables.We use this to show that, in certain cases, the only critical points of these functionals are minimizers. This approach based on displacement convexity permits us to treat multicomponent systems as well as single component systems. The developments produce new examples of displacement convex functionals and, in the multi-component setting, jointly displacement convex functionals.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-008-0190-9