Geodesic
Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 2, pp. 231-267 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14712/1213-7243.2019.010
Classification : 35B65, 35D30, 35K99
Keywords: nonlinear parabolic systems; regularity problem 
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Arkhipova, Arina A.; Stará, Jana. Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 2, pp. 231-267. doi: 10.14712/1213-7243.2019.010

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