Conical differentiability for evolution variational inequalities

The conical differentiability of solutions to the parabolic variational inequality with respect to the right-hand side is proved in the paper. From one side the result is based on the Lipschitz continuity in of solutions to the variational inequality with respect to the right-hand side. On the other side, in view of the polyhedricity of the convex cone we prove new results on sensitivity analysis of parabolic variational inequalities. Therefore, we have a positive answer to the question raised by Fulbert Mignot (J. Funct. Anal. 22 (1976) 25–32).