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Math Help - Lipschitz condition

  1. #1
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    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)| < A|y_1 - y_2|

    I have no idea how to find A though.
    Thanks!
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  2. #2
    MHF Contributor chisigma's Avatar
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    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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