Tuck the effected corners under the rug and leave like this for a few days then put back straight
You get double faced rug tape put it around the corners it sticks to the floor.
Try Duct or masking tape...not to stick it to the floor but turn it over....attach the duct tape to the outer edge of the under rug and pull it back until it curves just a wee bit. Not an extreme curve just a little....run the tape back a foot or two and flip it back over...maybe the pressure of the tape pulling will keep the corners from lifting. Good Luck!