Weakly monotone functions
Copyright policy )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.
- University of Pittsburgh United States
Regularity of generalized solutions of PDE, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, weakly monotone functions, Nonlinear elasticity, \(p\)-capacity, finite dilatation, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Maximum principles in context of PDEs
Regularity of generalized solutions of PDE, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, weakly monotone functions, Nonlinear elasticity, \(p\)-capacity, finite dilatation, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Maximum principles in context of PDEs
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