Assess graduate students' recall of foundational definitions and key properties of Sobolev spaces W^{k,p}(Ω) on open subsets of R^n: characterization of weak derivatives, construction and equivalence of Sobolev norms, completeness and density facts, precise statements and hypotheses of the Sobolev embedding theorems (including critical exponent relations) and the Rellich–Kondrachov compactness theorem; focus on correct formulations and immediate corollaries.