Abstract We study the boundary regularity of local weak solutions to nonlinear parabolic systems of the form aligned ₜ uⁱ - div (a (|Du|) Duⁱ) = fⁱ, i=1, , N, aligned in a space-time cylinder T = (0, T), where Rⁿ (n 2) is a bounded, convex C² -domain and T>0. The inhomogeneity f= (f¹, , fN) belongs to L^n+2+ (T, RN) for some >0. The coefficients a: R>₀ R>₀ are of Uhlenbeck-type and satisfy a nonstandard (p, q) -growth condition with 2 p q < p + 4n+2. Our main result establishes a local Lipschitz estimate up to the lateral boundary for any local weak solution that vanishes on the lateral boundary of the cylinder.
Michael Strunk (Tue,) studied this question.