Rellich–Kondrachov Compactness
On a bounded open domain, bounded families in the zero-boundary-value Sobolev space gain strong subsequential convergence below the critical exponent. Follow the translation estimates that turn derivative control into compactness.
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Start here: Notes on Partial Differential Equations
John K. Hunter · Lecture notes · English · Free full text
§3.10 Compactness results, Theorem 3.45 and its proof, printed pp. 73–75
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