Bunting identity and Mazur identity for non-linear elliptic systems including the black hole equilibrium problem

Recent work by G. Bunting and by P.O. Mazur has developed new techniques for proving uniqueness theorems for extensive classes of non-linear elliptic boundary value problems including that of the equilibrium state of an electromagnetically charged black hole. These methods are described and compared. It is shown that the rather general class of harmonic mappings that can be dealt with by the Bunting method (which needs no internal symmetry group) can be regarded as a generalisation of the particular (totally symetric) class of non-linear sigma-models that can be dealt with by the Mazur method. (orig.)