Is it permissible to give money from Zakat to well-off university students to encourage them?

The recipients of zakat (definition) are specified in the verse: "Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the traveler." Zakat may not be given to those other than these recipients. Therefore, giving it for the purpose mentioned (to a student of knowledge who is not eligible or to those outside the specified recipients) is not sufficient.