I am currently collecting data for a project investigating whether obligatory environments for genitive or possessive 's marking exist in African American English (AAE). In the variety, possessive marking is optional meaning the following sentences are both grammatical, and have the same meaning.
I am testing whether genitive marking is obligatory in the context of NP ellipsis or when the following noun is omitted.
Pilot data seem to suggest that with ellipsis, genitive marking is highly a preferred if not obligatory. I am now working with children at The Early Childhood Centers of Greater Springfield to see what they have to say about Joe cup. Stay tuned.