Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials

We prove higher integrability and differentiability results for local minimizers u: ${\mathbb {R}^2\supset\Omega\to\mathbb {R}^M}$ , M ≥ 1, of the splitting-type energy ${\int_{\Omega}h_1(|\partial_1 u|)+h_2(|\partial_2 u|)]\,{\rm d}x}$ . Here h ₁, h ₂ are rather general N-functions and no relation between h ₁ and h ₂ is required. The methods also apply to local minimizers u: ${\mathbb {R}^2\supset\Omega \to \mathbb {R}^2}$ of the functional ${\int_{\Omega}h_1(|{\rm div}\,{\rm u}|)+h_2(|\varepsilon^D(u)|)]\,{\rm d}x}$ so that we can include some variants of so-called nonlinear Hencky-materials. Further extensions concern non-autonomous problems.