Partial regularity for subquadratic parabolic systems by $\mathcal{A}$-caloric approximation

Abstract

We establish a partial regularity result for weak solutions of nonsingular parabolic systems with subquadratic growth of the type

where the structure function $a$ satisfies ellipticity and growth conditions with growth rate $\frac{2n}{n+2}<p<2$. We prove Hölder continuity of the spatial gradient of solutions away from a negligible set. The proof is based on a variant of a harmonic type approximation lemma adapted to parabolic systems with subquadratic growth.