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9
votes
1answer
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Prove that $\int_0^1|f''(x)|dx\ge4.$
Let $f$ be a $C^2$ function on $[0,1]$. $f(0)=f(1)=f'(0)=0,f'(1)=1.$ Prove that
$\int_0^1|f''(x)|dx\ge4.$
Also determine all possible $f$ when equality occurs.
2
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0answers
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An application of Poincare inequality [solved]
I am woking on Evans PDE problem 5.10. #15: Fix $\alpha>0$ and let $U=B^0(0,1)\subset \mathbb{R}^n$. Show there exists a constant $C$ depending only on $n$ and $\alpha$ such that
$$
\int_U u^2 dx ...
