  We approximate the solution to some linear and degenerate quasi-linear
problem involving a linear elliptic operator (like the semi-discrete in time
implicit Euler approximation of Richards and Stefan equations) with measure
right-hand side and heterogeneous anisotropic diffusion matrix. This
approximation is obtained through the addition of a weighted p--Laplace term. A
well chosen diffeomorphism between R and (--1, 1) is used for the estimates of
the approximated solution, and is involved in the above weight. We show that
this approximation converges to a weak sense of the problem for general
right-hand-side, and to the entropy solution in the case where the
right-hand-side is in L 1 .
