# Model problems from nonlinear elasticity: partial regularity results

Menita Carozza; Antonia Passarelli di Napoli

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 1, page 120-134
- ISSN: 1292-8119

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topCarozza, Menita, and Passarelli di Napoli, Antonia. "Model problems from nonlinear elasticity: partial regularity results." ESAIM: Control, Optimisation and Calculus of Variations 13.1 (2007): 120-134. <http://eudml.org/doc/250002>.

@article{Carozza2007,

abstract = {
In this paper we prove that every weak
and strong local
minimizer $u\in\{W^\{1,2\}(\Omega,\mathbb\{R\}^3)\}$ of the functional
$I(u)=\int_\Omega|Du|^2+f(\{\rm Adj\}Du)+g(\{\rm det\}Du),$
where $ u:\Omega\subset\mathbb\{R\}^3\to \mathbb\{R\}^3$,
f grows like $|\{\rm Adj\}Du|^p$, g grows
like $|\{\rm det\}Du|^q$ and
1<q<p<2, is $C^\{1,\alpha\}$ on an open
subset $\Omega_0$ of Ω such that
$\{\it meas\}(\Omega\setminus \Omega_0)=0$. Such
functionals naturally arise from nonlinear elasticity problems. The key
point in order to obtain the partial regularity result is to
establish an energy estimate of Caccioppoli type, which is based on
an appropriate choice of the test functions. The limit case
$p=q\le 2$
is also treated for weak local minimizers.
},

author = {Carozza, Menita, Passarelli di Napoli, Antonia},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Nonlinear
elasticity; partial regularity; polyconvexity.; Nonlinear elasticity; polyconvexity},

language = {eng},

month = {2},

number = {1},

pages = {120-134},

publisher = {EDP Sciences},

title = {Model problems from nonlinear elasticity: partial regularity results},

url = {http://eudml.org/doc/250002},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Carozza, Menita

AU - Passarelli di Napoli, Antonia

TI - Model problems from nonlinear elasticity: partial regularity results

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/2//

PB - EDP Sciences

VL - 13

IS - 1

SP - 120

EP - 134

AB -
In this paper we prove that every weak
and strong local
minimizer $u\in{W^{1,2}(\Omega,\mathbb{R}^3)}$ of the functional
$I(u)=\int_\Omega|Du|^2+f({\rm Adj}Du)+g({\rm det}Du),$
where $ u:\Omega\subset\mathbb{R}^3\to \mathbb{R}^3$,
f grows like $|{\rm Adj}Du|^p$, g grows
like $|{\rm det}Du|^q$ and
1<q<p<2, is $C^{1,\alpha}$ on an open
subset $\Omega_0$ of Ω such that
${\it meas}(\Omega\setminus \Omega_0)=0$. Such
functionals naturally arise from nonlinear elasticity problems. The key
point in order to obtain the partial regularity result is to
establish an energy estimate of Caccioppoli type, which is based on
an appropriate choice of the test functions. The limit case
$p=q\le 2$
is also treated for weak local minimizers.

LA - eng

KW - Nonlinear
elasticity; partial regularity; polyconvexity.; Nonlinear elasticity; polyconvexity

UR - http://eudml.org/doc/250002

ER -

## References

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