Weakly Differentiable Mappings Between Manifolds

The authors study Sobolev classes of weakly differentiable mappings $f:{\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}{1,n}({\mathbb X}\, ,\, {\mathbb Y})\,$, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed are: