Strongly Nonlinear Parabolic Variational Inequalities

In the present paper we deal with the existence of weak solutions of strongly nonlinear variational inequalities of parabolic operators of the form ∂u(x, t)∂t + Au(x, t), (x, t) ∈ Q = Ω × (0, T)u(0) = 0, where Au(x, t) = ∑Ni=1DiAi(x, t, Diu(x, t)) + A0(x, t, u(x, t)) is strongly nonlinear in the sense that its coefficients have a liberal growth. Although we restrict ourselves to second-order operators, our results are still workable for higher order operators.