  We consider the problem of determining the unknown boundary values of a
solution of an elliptic equation outside a bounded domain $B$ from the
knowledge of the values of this solution on a boundary of an arbitrary bounded
domain surrounding $B$. We obtain for this inverse problem Lipschitz stability
for an admissible class of unknown boundary functions. Our analysis applies as
well to an interior problem. We also give an extension to the parabolic case.
