I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 1 Calculational Linear Algebra.
 2 Wavelet Analysis.
 3 Finite element method.
 4 Construction of approximation spaces.
 5 Time discretization.
 6 Variational inequalities.
 A. Stationary variational inequalities.
 a. Weak and strong formulations for stationary variational inequality problem.
 b. Existence and uniqueness for coercive stationary problem.
 c. Penalized stationary problem.
 d. Proof of existence for stationary problem.
 e. Estimate of penalization error for stationary problem.
 f. Monotonicity of solution of stationary problem.
 g. Existence and uniqueness for non-coercive stationary problem.
 B. Evolutionary variational inequalities.
 VIII. Bibliography
 Notation. Index. Contents.

## Monotonicity of solution of stationary problem.

roposition

(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:

Proof

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 )

 Notation. Index. Contents.