Abstract
We prove a C 2,α partial regularity result for local minimizers of polyconvex variational integrals of the type \({I(u)=\int_\Omega |D^{2}u|^2+g({\det}(D^2u))dx}\), where Ω is a bounded open subset of \({ \mathbb {R}^{2}}\), \({u\in W_{loc}^{2,2}(\Omega)}\) and \({g\in C^{2}(\mathbb {R})}\) is a convex function, with subquadratic growth.
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Carozza, M., Leone, C., Passarelli di Napoli, A. et al. Partial regularity for polyconvex functionals depending on the Hessian determinant. Calc. Var. 35, 215–238 (2009). https://doi.org/10.1007/s00526-008-0203-4
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DOI: https://doi.org/10.1007/s00526-008-0203-4