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The co-area formula for Sobolev mappings |
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| Authors: | Jan Maly David Swanson William P. Ziemer |
| Affiliation: | Faculty of Mathematics and Physics, Charles University -- KMA, Sokolovská 83, 18675 Praha 8, Czech Republic ; Department of Mathematics, Texas A{&}M University, College Station, Texas 77843 ; Department of Mathematics, Indiana University, Bloomington, Indiana 47405 |
| Abstract: | We extend Federer's co-area formula to mappings  belonging to the Sobolev class  ,  ,  , and more generally, to mappings with gradient in the Lorentz space  . This is accomplished by showing that the graph of  in  is a Hausdorff  -rectifiable set. |
| Keywords: | Sobolev mapping Orlicz space co-area formula area formula rectifiability |
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