Does inverse inequality
$\|\nabla u\|_{L^{2}(\Omega)} \leq c_{inv}h^{-1} \|u\|_{L^{2}(\Omega)}$
on the spatial domain, $\Omega$ at least for a smooth domain exist?
2026-04-07 00:21:33.1775521293
Does inverse inequality on spatial domain at least for smooth domain exist?
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No. This cannot work. Think of $\Omega=(0,1)$ and $u_n(x):=\sin(n\pi x)$.