YA Apocalyptic - upper society has brain implants and outside of city is lawless/Mad Max style

[Ruth]

Read this maybe 20 years ago; and I've looked everywhere to find it. In the story, the main character is an outcas/thief; he falls in love with a girl from the city. The city is where the upper classes live, and is maybe set out in circles. Outside the walls is a waste land, dominated by Mad Max-style violent gangs with crazy vehicles. He rescues the girl when they remove her brain chip (?), Which you can upgrade if you are rich enough. This turns her into someone with the facilities of a baby, and they dump her alive into the sea (where he rescues her).
There may be more than one book; and at some point, they're in a cave. That's all I remember

[Kris]

The Outcast by Patricia Bernard?

Here's a discussion about this book - https://www.goodreads.com/topic/show/...

[Lobstergirl, au gratin]

Ruth, are you still looking for this or did you find it?