Calculus of Variations and Geometric Measure Theory

M. Carozza - L. Esposito - L. Lamberti

Quasiconvex Bulk and Surface Energies: $C^{1,\,\alpha}$ Regularity

created by lamberti on 27 Jul 2023



Inserted: 27 jul 2023
Last Updated: 27 jul 2023

Year: 2023


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