Partial regularity for subquadratic parabolic systems by A-caloric approximation

Abstract

We establish a partial regularity result for weak solutions of nonsingular parabolic systems with subquadratic growth of the type ∂tu - div a(x, t, u, Du) = B(x, t, u, Du) where the structure function a satisfies ellipticity and growth conditions with growth rate 2nn+2 < p < 2. We prove Holder 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.