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"Sobolev spaces" as a book category collects rigorous textbooks and monographs about the theory and applications of Sobolev spaces (W^{k,p}, H^s and their variants): definitions via weak derivatives, norms and dual spaces, embedding and compactness theorems, trace and extension results, interpolation and fractional-order spaces, and regularity and variational methods for elliptic, parabolic and hyperbolic PDEs. Books in this category range from introductory graduate texts that build the necessary measure-theoretic and functional-analytic prerequisites to advanced monographs treating fine regularity, spectral theory, calculus of variations, and numerical applications such as finite element analysis. Typical readers are advanced undergraduates, graduate students, and researchers in mathematics, physics, and engineering; adjacent categories include partial differential equations, functional analysis, harmonic analysis, and numerical analysis.

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