Lipschitz regularity for solutions of a general class of elliptic equations

We prove local Lipschitz regularity for local minimisers of $$W^{1,1}(\mathrm{\Omega })\ni v\mapsto {\int }_{\mathrm{\Omega }}F(Dv)dx$$ where $\mathrm{\Omega }\subseteq {\text{R}}^N$, $N\ge 2$ and $F:{\text{R}}^N\to \text{R}$ 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 $D^{2}F$ 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.