On equicontinuity of homeomorphisms with finite distortion in the plane

Abstract

It is stated equicontinuity and normality of families ${\mathfrak{F}}^{\Phi }$ of the so--called homeomorphisms with finite distortion on conditions that $K_f(z)$ has finite mean oscillation, singularities of logarithmic type or integral constraints of the type $\int \Phi \left(K_f(z)\right)dxdy<\infty$ in a domain $D\subset{\C}.$ It is shown that the found conditions on the function $\Phi$ are not only sufficient but also necessary for equicontinuity and normality of such families of mappings.

18 pages

References in corpus (2)

• Equicontinuity of mappings quasiconformal in the mean
• On homeomorphisms with finite distortion in the plane

Cited by in corpus (1)

• On mappings in the Orlicz-Sobolev classes