English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study homeomorphisms h : X onto −→ Y between two bounded domains in Rn having finite conformal energy E[h] = ∫ X ||Dh(x) || n dx < ∞ , h ∈ W (X,Y). 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 hj : 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.

Deformations of finite conformal energy: Boundary behavior and limit theorems