  The present paper aims at representing an improvement of the result in [2],
where a strong unique continuation property and a description of the local
behaviour around the edge of a crack for solutions to an elliptic problem are
established, by relaxing the star-shapedness condition on the complement of the
crack. More specifically, this assumption will be dropped off by applying a
suitable diffeomorphism which straightens the boundary of the crack, before
performing the approximation procedure developed in [2] in order to derive a
suitable monotonicity formula. This will yield the appearence of a matrix in
the equation, which shall be handled appropriately: for this we will take a
hint from [4].
