Regularity of Solutions to a Model Oblique Derivative Problem for Quasilinear Parabolic Systems with Nondiagonal Principal Matrices
Arina Alexeevna Arkhipova, G. V. Grishina · Vestnik St Petersburg University Mathematics · 2019
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.