We work on a bounded smooth domain. Let $C_0(\bar\Omega)$ be the set of continuous functions with compact support and let $s \in (0,1)$.
Is $H^s(\Omega) \cap C_0(\bar\Omega) \subset H^s(\Omega)$ dense?
I cannot find any reference..
2026-04-26 09:09:51.1777194591
Is $H^s(\Omega) \cap C_0(\bar\Omega) \subset H^s(\Omega)$ dense?
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Did you check Partial Differential Equations of Evans ? It is one of the best reference I've read on the subject.