The estimation of the area of a disk image for Sobolev classes

2016/04/26 by Bilet, V., Salimov, R.
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.07618

Abstract

For regular homeomorphisms of Sobolev class W^1,1_\textrmloc having the Luzin N-property, it is established the estimation of the area of a disk image in terms of an angular dilatation. As a corollary, the analog of the well-known Ikoma-Schwartz lemma for such mappings is obtained.

Related

• Lower bounds for areas of images of discs
• Hausdorff measure of critical set for Luzin N condition
• Characterizing Sobolev Homeomorphic Extensions via Internal Distances
• Foward the theory of Sobolev's mappings on the plane
• The refined area formula for Sobolev mappings W^k,p