Is there a standard definition of the function class $C^{1,2}$?

Question

If we're strictly talking about functions of class $C^1$ or $C^2$ then as far as I'm aware the definition on Wikipedia is totally standard, but can the same be said for $C^{1,2}$? In this particular case I can't tell if there's a lack of a standard or a lack of Googling skill on my part. The definition that I'm familiar with claims that all of the first-order partial derivates of the functions f(x,y) in the class exist and are continuous and also claims the same for the second partial derivate with respect to the second parameter of the functions.

Answer 1

I don't think there is a canonical meaning of $ C^{1,2} $.

Personally I have used this notation to mean that all partial derivatives exist that include at most one derivative with respect to the first and at most two derivatives with respect to the second variable, which is more restrictive than your definition