Ususally Sobolev spaces are defined for open domains but in some cases it would be handy to define them on compact domains. It doesn't actually matter, no? Because the boundary at the end is nothing but a set of measure zero. Or why do they bother to distinguish between open or not open sets here anyway.
2026-04-07 23:18:24.1775603904
Why is the domain of Sobolev spaces often defined to be open?
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