
Lipschitz condition
Does the function F(x,y) = xy^(1/3) satisfy a Lipschitz condition on the rectangle {(x,y) : x≤h, y≤k}?
I understand a function being Lipschitz to mean that there exists a positive constant A such that:
f(x,y_1)  f(x,y_2) < Ay_1  y_2
I have no idea how to find A though.
Thanks! :)

The Lipschitz condition...
$\displaystyle f(x,y_{1})  f(x,y_{2})< A\cdot y_{1}y_{2}$
... means pratically that in all D is...
$\displaystyle \frac{d f}{d y} < A$
... i.e. the partial derivative of f(*,*) respect to y is bounded in all D. In this case is $\displaystyle f(x,y) = (xy)^{\frac{1}{3}}$ and the partial derivative respect to y is umbounded...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$