Partial regularity for degenerate systems of double phase type

We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by $H(x,t)=t^p+a(x)t^q$ with $1<p\leq q$ and $a(x)$ a nonnegative $C^{0,\alpha}$-continuous function. Our main result proves that if $\frac{q}{p}\leq 1+\frac{\alpha}{n}$, the gradient of any weak solution is locally H\"older continuous, except on a set of measure zero.