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.
Quasiconvex bulk and surface energies: C1,α regularity
Luca Esposito;Lorenzo Lamberti
2024
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 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.File in questo prodotto:
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