Suggest Treatment For Dry Patches On The Elbow , Knees And Buttocks

I have EXTREMELY dry patches (tough leather-like with peeling skin) on both of my elbows, knees, arch of both feet, and on both sides of buttock. Despite using lotions, even Vasoline and triple antibiotic creams, the patches remain. Why I they appearing, and what can I do to get rid of them?