  The functionals of double phase type \[ \mathcal{H} (u):= \int \left(|Du|^{p}
+ a(x)|Du|^{q} \right) dx, ( q > p > 1, a(x)\geq 0) \] are introduced in the
epoch-making paper by Colombo-Mingione for constants $p$ and $q$, and
investigated by them and Baroni. They obtained sharp regularity results for
minimizers of such functionals. In this paper we treat the case that the
exponents are functions of $x$ and partly generalize their regularity results.
