Quasiconvex bulk and surface energies: C1,α regularity

Abstract

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 pp-growth, p≥2p\ge 2, without any further structure conditions. The anisotropic surface energy is defined by means of an elliptic integrand Φ\Phi not necessarily regular. For a minimal configuration (u,E)\left(u,E), we prove partial Hölder continuity of the gradient ∇u\nabla u of the deformation.

Keywords

• regularity
• nonlinear variational problem
• free interfaces
• 49n15
• 49n60
• 49n99