I disagree with the cost-sharing idea.
It sounds like your son does NOT live with you. If he lived with you, the MAYBE cost-sharing could work (although I still think in many cases it would not be allowable). But not living with you? No way. He is paying you to live there (by paying the mortgage). Just like a non-related party, that is rent.
No, if the rent is significantly below Fair Market Value, those expenses are not deductible.
