Submonotone Subdifferentials of Lipschitz Functions
Jonathan E. Spingarn · Transactions of the American Mathematical Society · 1981
The class of "lowwer-${C^1}$" functions, that is functions which arise by taking the maximum of a compactly indexed family of ${C^1}$ functions, is characterized in terms of properties of the generalized subdifferential. A locally Lipschitz function is shown to be lower-${C^1}$ if and only if its subdifferential is "strictly submonotone". Other properties of functions with "submonotone" subdifferentials are investigated.