(Assumption of coercivity 1) There is a number such that

(Existence and uniqueness for stationary problem) If the coefficients of satisfy the definition ( Elliptic differential operator ) and the condition ( Assumption of coercivity 1 ) then the problem ( Stationary variational inequality problem ) has a unique solution.

We prove uniqueness. The proof of existence is postponed until the section ( Proof of existence for stationary problem ).

Assume that there are two solutions and : We set in and in and add the results Hence, by the condition ( Assumption of coercivity 1 ) Thus