  We prove $C^{1,\nu}$ regularity for local minimizers of the \oh{multi-phase}
energy: \begin{flalign*} w \mapsto
\int_{\Omega}\snr{Dw}^{p}+a(x)\snr{Dw}^{q}+b(x)\snr{Dw}^{s} \ dx,
\end{flalign*} under sharp assumptions relating the couples $(p,q)$ and $(p,s)$
to the H\"older exponents of the modulating coefficients $a(\cdot)$ and
$b(\cdot)$, respectively.
