Real Analysis Exchange

Differentiability of Monotone Sobolev Functions

Jani Onninen

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We establish a sharp integrability condition on the partial derivatives of a weakly monotone Sobolev function to guarantee differentiability almost everywhere.

Article information

Real Anal. Exchange, Volume 26, Number 2 (2000), 761-772.

First available in Project Euclid: 27 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26B35: Special properties of functions of several variables, Hölder conditions, etc. 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Differentiability weakly monotonicity Lorentz spaces


Onninen, Jani. Differentiability of Monotone Sobolev Functions. Real Anal. Exchange 26 (2000), no. 2, 761--772.

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