If I were you I would apply eye cream on the entire eye area. Under my eyes,on the eyelids,under the eyebrows and in the corners of my eyes. I'm not sure if that is the best way to do but that is what I think anyway.
I found this on the Beauty Tips section on
http://www.principessabeauty.com
"#6 When applying cream or concealer to the delicate eye area, always use your ring or pinky finger as these fingers are weaker and more gentle. Never tug or rub!! Always pat gently."