Glaeser's continuity theorem

In mathematical analysis, Glaeser's continuity theorem, is a characterization of the continuity of the derivative of the square roots of functions of class C 2 . It was introduced in 1963 by Georges Glaeser, and was later simplified by Jean Dieudonné.

The theorem states: Let f   :   U → R + be a function of class C 2 in an open set U contained in R n , then f is of class C 1 in U if and only if its partial derivatives of first and second order vanish in the zeros of f.