Lipschitz regularity for solutions of a general class of elliptic equations

We prove local Lipschitz regularity for local minimisers of \[ W^{1,1}(\Omega)\ni v\mapsto \int_\Omega F(Dv)\, dx \] where $\Omega\subseteq \R^N$, $N\ge 2$ and $F:\R^N\to \R$ is a quasiuniformly convex integrand in the sense of [Kovalev and Maldonado, 2005], i.e.,a convex $C^1$-function such that the ratio between the maximum and minimum eigenvalues of $D^2F$ is essentially bounded. This class of integrands includes the standard functions $F(z)=|z|^p$ for any $p>1$ and arises as the closure, with respect to a natural convergence, of the strongly elliptic integrands of the Calculus of Variations.