(Monotonicity of solution of stationary problem) If the coefficients of satisfy the definition ( Elliptic differential operator ) and the condition ( Assumption of coercivity 1 ) then the operator (see the problem ( Stationary variational inequality problem )) is monotonous:

We use the equation with and . Note that in both cases . We have We subtract and obtain thus and by the condition ( Assumption of coercivity 1 )