Pointwise inequalities for Sobolev functions on outward cuspidal domains

TL;DR

This paper characterizes Sobolev spaces on cuspidal symmetric domains using pointwise inequalities, establishing their equivalence with Hajlasz-Sobolev spaces, thereby advancing the understanding of function spaces on singular domains.

Contribution

It provides a new characterization of Sobolev spaces on cuspidal domains through pointwise inequalities, linking them to Hajlasz-Sobolev spaces.

Findings

Sobolev spaces on cuspidal domains are characterized by pointwise inequalities

Sobolev spaces coincide with Hajlasz-Sobolev spaces on these domains

The approach advances analysis on singular geometric structures

Abstract

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.