  In this paper, we deal with an elliptic problem with the Dirichlet boundary
condition. We operate in Sobolev spaces and the main analytic tool we use is
the Lax-Milgram lemma. First, we present the variational approach of the
problem which allows us to apply different functional analysis techniques. Then
we study thoroughly the well-posedness of the problem. We conclude our work
with a solution of the problem using numerical analysis techniques and the free
software freefem++.
