The extension property for domains with one singular point

An arbitrary outward cuspidal domain is shown to be bi-Lipschitz equivalent to a Lipschitz outward cuspidal domain via a global transformation. This allows us to extend earlier Sobolev extension results on Lipschitz outward cuspidal domains from the work of Maz’ya and Poborchi to general outward cuspidal domains. We also establish a limit case of the extension results on outward cuspidal domains.