Absolutely Continuous Functions of Several Variables

A class of “absolutely continuous functions” ofnvariables is introduced. The absolute continuity implies continuity, weak differentiability with gradient inLn, differentiability almost everywhere, area, coarea and degree formulae. This gives a unified approach to some previously known conditions for...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 231; no. 2; pp. 492 - 508
Main Author: MALY, J
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.03.1999
Elsevier
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Real functions
Sciences and techniques of general use
Absolute continuity
Real function
N variable function
Differentiability
Hausdorff space
Jacobi matrix
Rado Reichelderfer condition
Continuity (mathematics)
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:A class of “absolutely continuous functions” ofnvariables is introduced. The absolute continuity implies continuity, weak differentiability with gradient inLn, differentiability almost everywhere, area, coarea and degree formulae. This gives a unified approach to some previously known conditions for the mentioned results based on monotonicity, finite dilatation or higher integrability of the gradient.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1998.6246