Partial regularity for degenerate systems of double phase type

Abstract

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