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edited Jul 31, 2020 at 8:28

R.P.

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Are there $f, g$ such that $$\int_$\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-2\int_{S^{1}}f'g<0,$$$ where $f'=\frac{\partial f}{\partial \theta}$

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asked Jul 31, 2020 at 6:33

liding

Are there $f, g$ such that $$\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-2\int_{S^{1}}f'g<0,$$ where $f'=\frac{\partial f}{\partial \theta}$

Let $f,g$ are the functions of $S^{1}$. Are there $f, g$ such that $$\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-2\int_{S^{1}}f'g<0,$$ where $f'=\frac{\partial f}{\partial \theta}$?

real-analysis ap.analysis-of-pdes