An inverse Sobolev lemma

Abstract

We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of \mathbb R^n to the full range 0 < p < n . As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of \mathbb R^n in terms of the growth of the mapping.

Locations

• Revista Matemática Iberoamericana - View - PDF