We prove an integral representation result for functionals with growth conditions which give coercivity on the space $SBD^p(Omega)$, for $OmegasubsetR^2$ a bounded open Lipschitz set, $pin(1,infty)$. The space $SBD^p$ of functions whose distributional strain is the sum of an $L^p$ part and a bounded measure supported on a set of finite $calH^{1}$-dimensional measure appears naturally in the study of fracture and damage models. Our result is based on the construction of a local approximation by $W^{1,p}$ functions. We also obtain a generalization of Korn's inequality in the $SBD^p$ setting.
Integral representation for functionals defined on $SBD^p$ in dimension two / Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 223:(2017), pp. 1337-1374. [10.1007/s00205-016-1059-y]
Integral representation for functionals defined on $SBD^p$ in dimension two
FOCARDI, MATTEO;
2017
Abstract
We prove an integral representation result for functionals with growth conditions which give coercivity on the space $SBD^p(Omega)$, for $OmegasubsetR^2$ a bounded open Lipschitz set, $pin(1,infty)$. The space $SBD^p$ of functions whose distributional strain is the sum of an $L^p$ part and a bounded measure supported on a set of finite $calH^{1}$-dimensional measure appears naturally in the study of fracture and damage models. Our result is based on the construction of a local approximation by $W^{1,p}$ functions. We also obtain a generalization of Korn's inequality in the $SBD^p$ setting.File | Dimensione | Formato | |
---|---|---|---|
Conti-Focardi-Iurlano_ARMA16.pdf
Accesso chiuso
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
981.99 kB
Formato
Adobe PDF
|
981.99 kB | Adobe PDF | Richiedi una copia |
int_repr-rev-final-VQR.pdf
accesso aperto
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
505.8 kB
Formato
Adobe PDF
|
505.8 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.