  In this paper we utilise new methods of Calculus of Variations in $L^\infty$
to provide a regularisation strategy to the ill-posed inverse problem of
identifying the source of a non-homogeneous linear elliptic equation,
satisfying Dirichlet data on a domain. One of the advantages over the classical
Tykhonov regularisation in $L^2$ is that the approximated solution of the PDE
is uniformly close to the noisy measurements taken on a compact subset of the
domain.
