Model problems from nonlinear elasticity : partial regularity results
ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 1, pp. 120-134.

In this paper we prove that every weak and strong local minimizer uW 1,2 (Ω, 3 ) of the functional I(u)= Ω |Du| 2 +f( Adj Du)+g( det Du), where u:Ω 3 3 , f grows like | Adj Du| p , g grows like | det Du| q and 1<q<p<2, is C 1,α on an open subset Ω 0 of Ω such that 𝑚𝑒𝑎𝑠(ΩΩ 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=q2 is also treated for weak local minimizers.

DOI: 10.1051/cocv:2007007
Classification: 35J50, 35J60, 73C50
Keywords: 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, Volume 13 (2007) no. 1, pp. 120-134. doi : 10.1051/cocv:2007007. http://archive.numdam.org/articles/10.1051/cocv:2007007/

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