Suppose $\Omega$ is bounded. Then, is it true that $W_0^{1,q}(\Omega)\subset W_0^{1,p}(\Omega)$ whenever $p\leq q$? It seems like it should certainly be true since we do know that $L^q(\Omega)\subset L^p(\Omega)$ under the same hypothesis. But I'm wondering if I'm missing a subtlety.
2026-04-25 18:16:05.1777140965
Sobolev space inclusions
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