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

Abstract

For regular homeomorphisms of Sobolev class $W_{\text{loc}}^{1,1}$ 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.

6 pages, in Russian