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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.

MSC:
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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