Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices

Abstract

Partial regularity of solutions to a class of second order nonlinear parabolic systems with non-smooth in time principal matrices is proved in the paper. The coefficients are assumed to be measurable and bounded in the time variable and VMO-smooth in the space variables uniformly with respect to time.

To prove the result, we apply the so-called A(t)-caloric approximation method. The method was applied by the authors earlier to study regularity of quasilinear systems.

Keywords

• nonlinear parabolic systems
• regularity problem