Mathematical analysis of the problem
Variational approach for the finite element method

It was implicitly assumed, when Theorems 1 and 2 were stated, that the solution to the problem existed; it was then shown with the result of Corollary 1 that, if it did exist, this solution was unique. This is an important point, as it provides a partial validation of the chosen model, insofar as the physicist always considers empirically that the phenomenon he is studying has a unique solution. Certainly, the study of the existence and uniqueness of the solution of a PDE problem is difficult and goes far beyond the scope of this article. However, in the case of the model problem, the existence and uniqueness of the solution of the minimization problem (1)...