Regularity for nonlinear variational inequalities of hyperbolic type

In this paper, we deal with the regularity for nonlinear variational inequalities of second order in Hilbert spaces with more general conditions on the nonlinear terms and without condition of the compactness of the principal operators. We also obtain the norm estimate of a solution of the given nonlinear equation on C([0,T];V)∩C1((0,T];H)∩C2((0,T];V∗)C([0,T];V)∩C1((0,T];H)∩C2((0,T];V∗) by using the results of its corresponding hyperbolic semilinear part.