Model Problems from Nonlinear Elasticity: Partial Regularity Results

Ω |Du| + f(AdjDu) + g(detDu), where u : Ω ⊂ IR → IR, f grows like |AdjDu|p, g grows like |detDu|q and 1 < q < p < 2, is C 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 test functions. The limit case p = q ≤ 2 is also treated for weak local minimizers. Mathematics Subject Classification. 35J50, 35J60, 73C50.