 Rellich proved the "L"2 theorem and Kondrashov the "L""p" theorem.Let Ω ⊆ R"n" be an open, bounded Lipschitz domain, and let 1 ≤ "p" 1,"p"(Ω; R) is continuously embedded in the "L""p" space "L""p"∗(Ω; R) and is compactly embedded in "L""q"(Ω; R) for every 1 ≤ "q" ∗.In symbols,

and

On a compact manifold with boundary, the Kondrachov embedding theorem states that if and then the Sobolev embedding

is completely continuous (compact).