Coarea Properties of Sobolev Functions

Jan Malý ()
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Jan Malý: Charles University in Prague, School of Mathematics, KMA

A chapter in Function Spaces, Differential Operators and Nonlinear Analysis, 2003, pp 371-381 from Springer

Abstract: Abstract The Lusin N-property is well known as a criterion for validity of theorems on change of variables in integral. Here we consider related properties motivated by the coarea formula. They also imply a generalization of Eilenberg’s inequality. We prove them for functions with gradient in the Lorentz space Lm,1. This relies on estimates of Hausdorff content of level sets for Sobolev functions and analysis of their Lebesgue points. A significant part of the presented results has its origin in a joint work with David Swanson and William P. Ziemer.

Keywords: Orlicz Space; Lorentz Space; Lebesgue Point; Young Function; Sobolev Function (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-8035-0_26

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DOI: 10.1007/978-3-0348-8035-0_26

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