I know that in $\mathbb{R}^2$, the immersion $$i: H^1(\Omega) \hookrightarrow L^4(\Omega) $$ is continuous. Is it also true when $\Omega = (0,1)$,i.e. an open interval in one dimension?
2026-03-28 21:06:24.1774731984
Is the immersion $i: H^1(\Omega) \hookrightarrow L^4(\Omega)$ continuous in $1D$?
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