This appendix provides a brief summary of definitions and facts about basic function spaces arising in the study of many partial differential equations (PDEs). Our main focus is on standard Sobolev spaces as well as some Hilbert spaces related to the gradient, curl, and divergence operators because these spaces are the most relevant ones to the subject matter of the book, namely the numerical solution of PDEs by least-squares finite element methods (LSFEMs). For more comprehensive treatments of the various function spaces arising in the theory of PDEs, see, e.g., [1, 17, 183, 187, 250, 265, 304, 331, 342].
KeywordsSobolev Space Function Space Weighted Space Weak Operator Weighted Sobolev Space
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