Weakly Differentiable Mappings Between Manifolds

The authors study Sobolev classes of weakly differentiable mappings $f: {mathbb X} ightarrow {mathbb Y}$ 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 a