Regularity for minimizers of scalar integral functionals with (p, q)-growth conditions

We prove the local Lipschitz regularity of the local minimizers of scalar integral functionals of the form \(\begin{aligned} {\mathcal {F}}(v;\Omega )= \int _{\Omega } f (x, Dv) dx \end{aligned}\) $$\begin{array}{c}\hfill \mathcal{F}(v;\mathrm{\Omega })={\int }_{\mathrm{\Omega }}f(x,Dv)dx\end{array}$$ under (p, q)-growth conditions. The main novelty is that, beside a suitable regularity assumption on the partial map \(x\mapsto f(x,\xi )\) $x\mapsto f(x,\xi )$ , we do not assume any special structure for the energy density as a function of the \(\xi \) $\xi$ -variable.