Quasiconvex bulk and surface energies: C1,α regularity

We establish regularity results for equilibrium configurations of vectorial multidimensional variational problems, involving bulk and surface energies. The bulk energy densities are uniformly strictly quasiconvex functions with p p -growth, p ≥ 2, without any further structure conditions. The anisotropic surface energy is defined by means of an elliptic integrand φ not necessarily regular. For a minimal configuration (u, E), we prove partial Hölder continuity of the gradient ∇ u of the deformation.