Preprint

Inserted: 27 jul 2023
Last Updated: 27 jul 2023

Year: 2023

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

Keywords: regularity, nonlinear variational problem, Free interfaces

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• Quasiconvex Bulk and Surface Energies