On mappings whose inverses satisfy the Poletsky inequality
Evgeny Sevost’yanov, Sergei Skvortsov
Abstract
The article investigates mappings whose inverses distort the modulus of paths similarly to the Poletsky inequality. It is proved that the classes of such mappings form equicontinuous families if the majorant corresponding to the distortion of the module is integrable in the domain of their definition. Under additional conditions on the geometry of the domain of definition and the image domain these families are equicontinuous, not only at inner, but also at boundary points. In addition, the question of removability of the isolated singularities for such mappings is resolved.
Topics & Concepts
InequalityMathematicsPure mathematicsAlgebra over a fieldMathematical economicsCalculus (dental)Mathematical analysisMedicineDentistryAnalytic and geometric function theoryMathematical Inequalities and ApplicationsFunctional Equations Stability Results