Partial regularity for subquadratic parabolic systems with continuous coefficients

Abstract

We establish the partial regularity of solutions to quasilinear parabolic systems with elliptic part that grows subquadratically. More precisely, it is shown that there is an open subset with full measure, of the solution’s domain, on which the solution is Holder continuous. A key feature in this article is that we only require the coefficients of the system to be continuous with respect to the first two arguments. To prove the result, we use the A-caloric approximation method and an intrinsic scaling. To accommodate the subquadratic growth an adaptation of the A-caloric approximation lemma is also provided.