Regularity of Solutions to a Model Oblique Derivative Problem for Quasilinear Parabolic Systems with Nondiagonal Principal Matrices.

Autor: Arkhipova, A. A., Grishina, G. V.
Zdroj: Vestnik St. Petersburg University: Mathematics; Jan2019, Vol. 52 Issue 1, p1-18, 18p
Abstrakt: 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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