We study the asymptotic behavior, as tends to zero, of the functionals introduced by Coleman and Mizel in the theory of nonlinear second-order materials. By proving a new nonlinear interpolation inequality, we show a Γ-convergence result. Moreover, in the special case of the classical potential, we provide an upper bound on the values of k such that the minimizers of the functional cannot develop oscillations on some fine scale and a lower bound on the values for which oscillations occur, the latter improving a previous estimate by Mizel, Peletier and Troy.
Asymptotic analysis of a second-order singular perturbation model for phase transitions / Cicalese, M.; Spadaro, E. N.; Zeppieri, CATERINA IDA. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 41:1-2(2011), pp. 127-150. [10.1007/s00526-010-0356-9]
Asymptotic analysis of a second-order singular perturbation model for phase transitions
M. Cicalese;E. N. Spadaro;ZEPPIERI, CATERINA IDA
2011
Abstract
We study the asymptotic behavior, as tends to zero, of the functionals introduced by Coleman and Mizel in the theory of nonlinear second-order materials. By proving a new nonlinear interpolation inequality, we show a Γ-convergence result. Moreover, in the special case of the classical potential, we provide an upper bound on the values of k such that the minimizers of the functional cannot develop oscillations on some fine scale and a lower bound on the values for which oscillations occur, the latter improving a previous estimate by Mizel, Peletier and Troy.File | Dimensione | Formato | |
---|---|---|---|
Cicalese_Asymptotic-analysis_2011.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
334.3 kB
Formato
Adobe PDF
|
334.3 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.