Sobolev Extension on $L^p$-Quasidisks

In this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of the classical quasidisks. After that, we also find some applications of their Sobolev extension property.

Pointwise inequalities for Sobolev functions on outward cuspidal domains

We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spaces.