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An inequality for a two variable function

  1. Sep 30, 2013 #1
    Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that
    ##
    F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big).
    ##
     
  2. jcsd
  3. Oct 1, 2013 #2

    Simon Bridge

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    You'd start by considering what sort of curve is described by the part in parentheses in the second relation.
    What role does c play? Is there a minimum value that the first expression can take?
     
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