This article is cited in 2 scientific papers (total in 2 papers)
Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices
A. A. Arkhipova
Saint Petersburg State University
The Venttsel' problem in the model statement for quasilinear parabolic systems of equations with nondiagonal principal matrices is considered. It is only assumed that the principal matrices and the boundary condition are bounded with respect to the time variable. The partial smoothness of the weak solutions (Hölder continuity on a set of full measure up to the surface on which the Venttsel' condition is defined) is proved. The proof uses the $A(t)$-caloric approximation method, which was also used in  to investigate the regularity of the solution to the corresponding linear problem.
parabolic system of equations, partial smoothness of weak solutions, $A(t)$-caloric approximation method, Venttsel' problem.
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Computational Mathematics and Mathematical Physics, 2017, 57:3, 476–496
A. A. Arkhipova, “Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 470–490; Comput. Math. Math. Phys., 57:3 (2017), 476–496
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\paper Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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Arkhipova A.A., Grishina G.V., “Regularity of Solutions to a Model Oblique Derivative Problem For Quasilinear Parabolic Systems With Nondiagonal Principal Matrices”, Vestn. St Petersb. Univ.-Math., 52:1 (2019), 1–18
Arkhipova A.A., Stara J., “Regularity Problem For One Class of Nonlinear Parabolic Systems With Non-Smooth in Time Principal Matrices”, Comment. Math. Univ. Carol., 60:2 (2019), 233–269
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