A attestation on equability between a problem with obstacles on the boundary and a variational inequality

Contact problem widely exists in diverse fields.Many contact problems are induced to boundary values and variational problem.Boundary variational inequality methods have been playing crucial roles in contact problem field,inducing all the boundary conditions and contact conditions to one variational inequality and making the theoretical analysis very easy.Variational problem is a bridge to solve boundary values by variational inequality.In the paper,a function is derived on the base of the functional of po- tential energy,and their equivalence on a boundary value problem with obstacles on the boundary and equal variational problem is proved.So the partial differential equation's boundary value with obstacle can be solved by the corresponding variational problem.