Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition

Abstract

We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the Holder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.