Equicontinuity of mappings quasiconformal in the mean
V. Ryazanov, E. Sevost'yanov
TL;DR
This paper establishes necessary and sufficient criteria for the equicontinuity and normality of classes of space mappings with integral restrictions, with applications to Sobolev spaces.
Contribution
It provides a comprehensive set of criteria characterizing equicontinuity and normality for mappings quasiconformal in the mean, including necessary and sufficient conditions.
Findings
Criteria for equicontinuity and normality are both necessary and sufficient.
Applications to Sobolev classes demonstrate practical relevance.
The conditions extend understanding of quasiconformal mappings with integral restrictions.
Abstract
It is stated a series of criteria of equicontinuity and normality for classes of space mappings with integral restrictions. It is shown that the found conditions are not only sufficient but also necessary. It is given applications to Sobolev's classes.
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Taxonomy
TopicsAnalytic and geometric function theory · Differential Equations and Boundary Problems · Nonlinear Partial Differential Equations