Sobolev and Quasiconformal Extension Domains
Sobolev and Quasiconformal Extension Domains
A domain $D \subset {\mathbb {R}^n}$ has the quasiconformal extension property if each quasiconformal self-map of $D$ extends to a quasiconformal self-map of ${\mathbb {R}^n};\;D$ has the Sobolev extension property if there is a bounded linear operator $\Lambda :{W^{1,n}}(D) \to {W^{1,n}}({\mathbb {R}^n})$. We consider the relation between the above extension …