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.

Carlen, E.A., Carvalho, M.C., Esposito, R., Lebowitz, J.L., & Marra, R. (2009). Displacement Convexity and Minimal Fronts at Phase Boundaries. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 194(3), 823-847 [10.1007/s00205-008-0190-9].

Displacement Convexity and Minimal Fronts at Phase Boundaries

MARRA, ROSSANA
2009

Abstract

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - Fisica Matematica
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
eng
Con Impact Factor ISI
MODEL; TRANSITIONS; INTERFACE; SYSTEMS
Carlen, E.A., Carvalho, M.C., Esposito, R., Lebowitz, J.L., & Marra, R. (2009). Displacement Convexity and Minimal Fronts at Phase Boundaries. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 194(3), 823-847 [10.1007/s00205-008-0190-9].
Carlen, E; Carvalho, M; Esposito, R; Lebowitz, J; Marra, R
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/26233
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