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Evans
5 Sobolev spaces
5.2 Sobolev spaces
5.2.2 Defintion of Sobolev spaces
Appendix
A. Notation
A.1. Notation for matrices [Evans A1]
A.2. Geometric noation [Evans A2]
A.3. Notation for functions [Evans A3]
A.4. Vector-valued functions [Evans A4]
A.5. Notation for estimates [Evans A5]
A.6. Some comments about notation [Evans A6]
B. Inequalities
B.2. Useful inequalities
B.2.2 Cauchy's inequality with epsilon
B.2.4. Young's inequality with epsilon
B.2.7. General H"older inequality
B.2.8. Interpolation inequality for -norms
B.2.9. Cauchy-Schwarz inequality
B.2.10. Gronwall's inequality (differential form)
B.2.11. Gronwall's inequality (integral form)
C.3. Polar coordinates, coarea formula
C.5. Convolution and smoothing
C.7. Implicit function theorem
D. Functional Analysis
D.3.1. Linear operators on Banach spaces
D.3.2. Linear operators on Hilbert spaces
D.5. Compact operators, Fredholm theory
D.5.1 Definitions and basic properties
D.5.3. The spectrum of compact operators
E. Measure theory
E.2. Measurable functions and integration
E.3. Convergence theorems for integrals
E.5. Banach space-valued functions
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