On the convergence of mappings with \(k\)-finite distortion
The authors study classes of mappings with \(k\)-finite distortion, which are closely connected to the problem of pull-backs of differential \(k\)-forms. The main result states the lower semicontinuity of distortion coefficients under locally uniform convergence in the case of homeomorphisms with \(k\)-finite \((q,p)\)-bounded distortion. The obtained results are closely related to those from [the first author and \textit{A. O. Molchanova}, Sib. Math. J. 57, No. 5, 778--787 (2016; Zbl 1359.30040); translation from Sib. Mat. Zh. 57, No. 5, 999--1011 (2016)] and based on a method developed in the first author's work [Sib. Adv. Math. 14, No. 1, 84--125 (2004; Zbl 1076.30025)].
scientific article; zbMATH DE number 6845193