Model problems from nonlinear elasticity: partial regularity results

Menita Carozza, Antonia Passarelli di Napoli
2007 E S A I M: Control, Optimisation and Calculus of Variations  
In this paper we prove that every weak and strong local minimizer u ∈ W 1,2 (Ω, IR 3 ) of the functional where u : Ω ⊂ IR 3 → IR 3 , f grows like |AdjDu| p , g grows like |detDu| q and 1 < q < p < 2, is C 1,α on an open subset Ω0 of Ω such that meas(Ω \ Ω0) = 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
more » ... st functions. The limit case p = q ≤ 2 is also treated for weak local minimizers. Mathematics Subject Classification. 35J50, 35J60, 73C50.
doi:10.1051/cocv:2007007 fatcat:lflm3lavyjgina4w5vjgtzb5g4