Preprint

Inserted: 9 jan 2025
Last Updated: 9 jan 2025

Year: 2025

Abstract:

We establish partial Hölder continuity of the gradient 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, $1<p<2$, without any further structure conditions. The anisotropic surface energy is defined by means of an elliptic integrand $\Phi$ not necessarily regular.

Keywords: regularity, nonlinear variational problem, Free interfaces

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• CarozzaEspositoLamberti_Subquadratic.pdf