Weakly monotone functions
The definition of monotone function in the sense of Lebesgue is extended to the Sobolev spaces \(W^{1,p}\), \(p>n-1\). It is proven that such weakly monotone functions are continuous except in a singular set of \(p\)- capacity zero, that is empty in the case \(p=n\). Applications to the regularity of mappings with finite dilatation appearing in nonlinear elasticity theory are given.
scientific article; zbMATH DE number 653345