Untitled

Abstract

We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h : X → Y. In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms h j : X → Y one loses injectivity. However, if the mappings in question have uniformly bounded L 1-average of the inner distortion, then, for sufficiently regular domains X and Y, their limit map h : X onto −→ Y is a homeomorphism. Moreover, the inverse map f = h −1 : Y onto −→ X enjoys finite conformal energy and has integrable inner distortion as well.