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Thus Φ is coercive on E. By the coercivity of Φ, a Palais-Smale sequence { z n } of Φ must be bounded.
is coercive on.
Therefore is coercive on.
This implies that is coercive on.
To show that is coercive on, fix.
Let be uniformly coercive on with respect to.
f is coercive on (H_{tau}timescdotstimes H_{tau}).
We do not know whether I is coercive on ℳ.
Hence (mathcal{L}_{K}) is coercive on (W_{0}).
It remains to prove that I is coercive on X.
The functional I is (C^{1}) and coercive on X.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com