Nonsmooth Morse-Sard theorems

作者：Azagra D^*; Ferrera J; Gomez Gil J

来源：Nonlinear Analysis-Theory Methods & Applications, 2017, 160: 53-69.

DOI：10.1016/j.na.2017.05.006

• Morse-Sard theorem
• Taylor polynomial
• Subdifferential
• Nonsmooth

prove that every function f : R-n -> R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n - 1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof, for the proximal subdifferential partial derivative(p), we see that for every lower semicontinuous function f : R-2 -> R the set f({x is an element of R-2 : 0 is an element of partial derivative(p) f(x)}) is L-1-null.

• 出版日期2017-9