## Arina A. Arkhipova, Jana StarĂ¡

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

Comment.Math.Univ.Carolin. 60,2 (2019) 231-267.**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

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