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 <f>H<NU>1</NU>/2,1(Q)</f> 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 coneK={v∈H;v|Σc&ges;0,v|Σd=0},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). [Copyright &y& Elsevier]