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

Abstract

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 Holder continuity of solutions u∈W2t,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.