Given a function $u$ with compact support and a bounded area $\Omega\subset\mathbb{R}^n$ with $n \geq 3$. We have the well know Gagliardo–Nirenberg inequality $$ \|u\|_{L^2} \leq C \|Du\|_{L^2}. $$ What is the best (known) constant $C\in\mathbb{R}$, such that this inequality holds?
2026-04-25 00:37:21.1777077441
Best constants for Gagliardo–Nirenberg inequality in the case: p=q=2
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