How can I forward the user to the new DHCP address of the ESP?

[brianmichalk1]

Is there some facility, like the SSID scan, but at the DHCP layer where The ESP can get a short lease on an IP address, and show that to the user?
Ideally, this would be in the "web page unavailable" screen after the ESP switches to the new network, but that's perhaps impossible.
I was thinking about having the ESP send an SMS messge, or maybe it contacts my server, and my server sends the user an email with its new URL.
How does the mDNS work, if there's multiple servers on the network?
I'm thinking Android device here, where the user configures the ESP via captive portal, then the ESP switches to STA mode.