A mathematical problem related to the physical theory of liquid crystal configurations

It will turn out that one necessartly has to understand the structure of the set of singularities of functions of bounded variation. This was first studied by the fundamental work of DeGi orgi [ 16], [3] and H. Federer [7). (see also Vol'pert [ 15], ~:1d Simon [ 12]). In this note we shall explain a different method that we have used in order to study this basic fact and which is useful to study the li~uid crystal problem which we shall explain in Section 2. As a matter of fact we have recovered the well known results mentioned above and furthermore we have obtained new information that we shall be briefly discussing.