%0 Journal Article %A Ferrera Cuesta, Juan %A Gómez Gil, Javier %T Whitney's Theorem: A nonsmooth version %D 2015 %@ 0022-247X %U https://hdl.handle.net/20.500.14352/24119 %X In this paper we solve the problem of extending continuous functions with nonempty subdifferential at every point of a closed subset A of R-n to functions with the same property defined in the whole Rn, keeping the property of outer semicontinuity of the subdifferential, which is a set-valued function. The proof is constructive, and gives us a wide range of possible extensions. %~