On a partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth

Quasilinear nondiagonal parabolic systems with quadratic growth in the gradient in a parabolic cylinder Q are considered. Under Dirichlet and Neumann boundary conditions, a partial Hölder continuity of solutions u ε21,1(Q) ∩ L∞ (Q) up to the lateral surface of Q is proved. The Hausdorff dimension of a singular set is estimated. In the proof, we get rid of the maximum, principle theorem for respective model linear problems. Bibliography: 21 titles. © 2000 Kluwer Academic/Plenum Publishers.