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
DOI: DOI 10.14712/1213-7243.2019.010
AMS Subject Classification: 35B65 35D30 35K99