TY - JOUR

T1 - Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices

AU - Arkhipova, A. A.

AU - Grishina, G. V.

N1 - Arkhipova, A.A. & Grishina, G.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 1. https://proxy.library.spbu.ru:2060/10.3103/S1063454119010023

PY - 2019

Y1 - 2019

N2 - We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial Hölder continuity of a weak solution near the plane part of the lateral surface of the cylinder. Hölder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions.

AB - We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial Hölder continuity of a weak solution near the plane part of the lateral surface of the cylinder. Hölder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions.

KW - nonlinearity

KW - oblique derivative

KW - parabolic systems

KW - regularity

UR - http://www.scopus.com/inward/record.url?scp=85064894127&partnerID=8YFLogxK

U2 - 10.3103/s1063454119010023

DO - 10.3103/s1063454119010023

M3 - Article

VL - 52

SP - 1

EP - 18

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -