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Weakly monotone functions. (English) Zbl 0805.35013
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.

35B50Maximum principles (PDE)
74B20Nonlinear elasticity
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35D10Regularity of generalized solutions of PDE (MSC2000)
30C65Quasiconformal mappings in n and other generalizations
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