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Does coercivity/supercoercivity conjugates?

According to Wikipedia, a function $f: \mathbb{R}^n \to \mathbb{R} \cup \{-\infty, +\infty\}$ is called coercive if, $$f(x) \to +\infty \text{ as } \|x\| \to +\infty$$ and it is super-coercive if $$\...
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