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Math Help - Growth Condition

  1. #1
    Junior Member
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    Texas
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    Growth Condition

    Hello all,

    I'm working on a problem, that at the first step requires a growth estimate, that I can't seem to get. Here's the pertinent information:

    Let u\in C^2(\mathbb{R}) satisfying
    \lim_{|x|+|t|\to\infty}\frac{u(x,t)}{|x|^5+|t|^5}=  0.
    Show that there exists C>0 so that
    |u(x,t)|\leq C(1+|x|+|t|)^5
    for all x,t\in\mathbb{R}.

    Thanks for the help!
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  2. #2
    Junior Member
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    May 2010
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    Texas
    Posts
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    Re: Growth Condition

    Maybe this should be moved to Differential Geometry. I never thought of Analysis as a subset of Differential Geometry, and just posted this in Calculus choosing the more relevant section-title, without reading the subsections. Apologies if it matters at all.
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