Model problems from nonlinear elasticity : partial regularity results

Carozza, Menita; Passarelli Di Napoli, Antonia

doi:10.1051/cocv:2007007

Carozza, Menita ; Passarelli Di Napoli, Antonia

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 120-134.

Résumé

In this paper we prove that every weak and strong local minimizer $u \in W^{1, 2} (Ω, ℝ^{3})$ of the functional $I (u) = \int_{Ω} {| D u |}^{2} + f (Adj D u) + g (\det D u),$ where $u : Ω \subset ℝ^{3} \to ℝ^{3}$ , $f$ grows like ${| Adj D u |}^{p}$ , $g$ grows like ${| \det D u |}^{q}$ and $1 < q < p < 2$ , is $C^{1, α}$ on an open subset $Ω_{0}$ of $Ω$ such that $𝑚𝑒𝑎𝑠 (Ω ∖ Ω_{0}) = 0$ . 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 $p = q \leq 2$ is also treated for weak local minimizers.

MR | 1 citation dans Numdam

DOI : 10.1051/cocv:2007007

Classification : 35J50, 35J60, 73C50
Mots-clés : nonlinear elasticity, partial regularity, polyconvexity

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Carozza, Menita; Passarelli Di Napoli, Antonia. Model problems from nonlinear elasticity : partial regularity results. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 120-134. doi : 10.1051/cocv:2007007. https://www.numdam.org/articles/10.1051/cocv:2007007/

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