We establish a partial regularity result for weak solutions of nonsingular parabolic systems with subquadratic growth of the type
where the structure function satisfies ellipticity and growth conditions with growth rate . 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.
Cite this article
Christoph Scheven, Partial regularity for subquadratic parabolic systems by -caloric approximation. Rev. Mat. Iberoam. 27 (2011), no. 3, pp. 751–801DOI 10.4171/RMI/652