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 DieudonnÃ©.

The theorem states: Let
f
:
U
â†’
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*.