Strongly Nonlinear Parabolic Variational Inequalities

Abstract

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) = ∑ N i=1D iA i(x, t, D iu(x, t)) + A 0(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.