We study homeomorphisms h Y between two bounded domains in ℝn having finite conformal energy We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms h one loses injectivity. However, if the mappings in question have uniformly bounded ℒ1-average of the inner distortion, then, for sufficiently regular domains X and Y, their limit map h: X Y is a homeomorphism. Moreover, the inverse map f=h-1: Y X enjoys finite conformal energy and has integrable inner distortion as well.
- Boundary behavior of homeomorphisms
- Energy integrals
- Limit theorems
- Quasiconformal hyperelasticity
ASJC Scopus subject areas
- Applied Mathematics