Weakly monotone functions (Q1336081)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Weakly monotone functions |
scientific article; zbMATH DE number 653345
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weakly monotone functions |
scientific article; zbMATH DE number 653345 |
Statements
Weakly monotone functions (English)
0 references
1 February 1995
0 references
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.
0 references
\(p\)-capacity
0 references
weakly monotone functions
0 references
finite dilatation
0 references
