Anisotropic Sobolev homeomorphisms

Authors :: Luigi D'Onofrio
Patrizia Di Gironimo
Carlo Sbordone
Roberta Schiattarella
P., DI GIRONIMO
L., D'Onofrio
Sbordone, Carlo
Schiattarella, Roberta
Source :: Annales Academiae Scientiarum Fennicae Mathematica. 36:593-602
Publication Year :: 2011
Publisher :: Finnish Academy of Science and Letters, 2011.
Abstract: Let › ‰ R 2 be a domain. Suppose that f 2 W 1;1 loc (›;R 2 ) is a homeomorphism. Then the components x(w), y(w) of the inverse f i1 = (x;y): › 0 ! › have total variations given by jryj(› 0 ) = › fl fl @f fl fl dz; jrxj(› 0 ) = › fl fl @f @y fl fl dz