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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
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On Talenti's proof of optimal constant in Sobolev inequality
I'm reading the paper by Giorgio Talenti on the best constant for the Sobolev inequality.
The main theorem states that for $u:\mathbb{R}^m\rightarrow \mathbb{R}$ sufficiently smooth (eg. Lipschitz) an …