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

• Date: 2017
• Author Affiliations: — Ин-т прикладной математики и механики НАН Украины; — Институт математики НАН Украины; — Институт математики НАН Украины
• Keywords: keywords
• Main Authors: Bilet, V. V., Klishchyk, B. A., Salimov, R. R., Билет, В. В., Клищук, Б. А., Салимов, Р. Р.
• Format: Article
• Language: Russian
• Published: Інститут математики НАН України 2017
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/97
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

Lower and upper estimates of an area for image of a disk under regular homeomorphisms of the Sobolev class $W^{1,1}_{\textrm{loc}}$, havingthe Luzin $N$-property, are established in terms of an angular $p$-dilatation.