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Q: Improvement of isoperimetric inequalities

BazinThe standard functional isoperimetric inequality is for an integer $n\ge 1$, $$ \Vert u\Vert_{L^{\frac{n}{n-1}}(\mathbb R^n)}\le c(n)\Vert \nabla u\Vert_{L^1(\mathbb R^n)}, \quad c(n)=\frac{(\vert\mathbb B^n_2\vert_n)^{\frac{n-1}{n}}}{ \vert\mathbb S^{n-1}_2\vert_{n-1} }, \tag{$\flat$}$$ where $\...


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