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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