Lipschitz condition

**charlie** · October 19th 2009, 03:46 PM

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)| < A|y_1 - y_2|

I have no idea how to find A though.
Thanks!

**chisigma** · October 19th 2009, 10:14 PM

The Lipschitz condition...

$|f(x,y_{1}) - f(x,y_{2})|< A\cdot |y_{1}-y_{2}|$

... means pratically that in all D is...

$\frac{d f}{d y} < A$

... i.e. the partial derivative of f(*,*) respect to y is bounded in all D. In this case is $f(x,y) = (xy)^{\frac{1}{3}}$ and the partial derivative respect to y is umbounded...

Kind regards

$\chi$ $\sigma$

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