Nichibei Aviation,
To declare MayDay for an engine failure at take-off is not correct.This is my point of view.All modern airplanes are made to fly with one engine out.So if you depart from an airport wich is not suitable for landing due to weather(let s say visibility or other reason),you have to land on take -off alternate, right?
I remember a BA flight LAX-LHR , a year ago, they had an engine failure ,B 747-400, and did not return on L.A., they continued the flight with 3 valid engines (the flight had a stop before landing in London for refueling).