ERRATA to “INTRODUCTION TO
PARTIAL DIFFERENTIAL EQUATIONS” (2nd ed.)
G. B. Folland
Last updated September 6, 2017
Additional corrections will be gratefully received at folland@math.washington.edu .
Page 2, line −7: an → αn
Page 3, line 1 after “Function Spaces”: dente → denote
1/(1−t2 ) 1/(t2 −1)
Page 12, line 14: e → e
Page 16, line 5: reamins → remains
Page 18, line −6: graddaddy → granddaddy
Page 43, second-to-last displayed equation: ∂jt → ∂tj
Page 43, last displayed equation: |α|j → |αj |
Page 61, Lemma 1.53: You can replace (d/2) by dk , and the proof is trivial. (Exercise!)
k
Page 69, line 2: C 1 → C2
Page 77, line −7: Insert “the final paragraph of” before “§4B.”
Page 84, line 12: (2.31) → (2.32)
Page 87, line 7: δ(x, y) → δ(x − y)
Page 87, first line after Claim (2.38): calleed → called
Page 91, line 1: (2.37) → (2.40)
Page 97, second display in proof of Theorem 2.48: ωn−1 → ωn
Page 97, next line after preceding item: (2.44) → (2.46)
Page 99, line −10: Pk ∆P j → P k ∆Pj
Page 100, line −10: ser → set
Page 100, line −1: proerties → properties
n−1 n−1 0
Page 105, lines 9 and 14: → f (r)
r r
Page 109, Exercise 5, Hint: eiθ → eikθ
Page 112, line −5: corvilinear → curvilinear
Page 118, Remark, line 2: C 1 (Ω) → C 2 (Ω)
Page 119, last line of proof of Prop. 3.6: right → left
Page 121, line −3: (3.11) → (3.10)
Page 133, Exercise 1: The asserted formula for u(x) should be multiplied by Rn−1 (includ-
ing the case n = 2).
Page 134, Exercise 2: The integrand of the second integral should be f (y)N (y).
Page 145, line 4: K(x, t) → K(x − x0 , t0 − t) (two places)
Page 150, lines 1 and 2: kψ → κψ
1 2
R R
Page 173, formula (5.22): 1·3···(n−1) → 1·3···(n−1) and |y|=1
→ |y|≤1
Page 174, formula (5.24): ∂t u − ∆u → ∂t2 u − ∆u
Page 175, line 4 and line −3: ∂t v − ∆v → ∂t2 v − ∆v
Page 177, line −6: ∂t u
b(ξ, t) → ∂t u
b(ξ, 0)
Page 192, line 9: if → of
Page 192, line −3: at as → as
Page 194, line 3 of Proof: kf ks → Ckf ks
Page 195, next-to-last line of Remark 1: Example 1 → Example 2
Page 201, lines 9 and 11: fk → fbk
j j
2 s−1)/2
Page 203, line −8: (1 + t ) → (1 + t2 )(s−1)/2
Page 204, line −4: u → f
Page 205, lines 5, 7, and 8: u → f
Page 207, line 2: kφks−x → kφks+x
Page 208, line 6: There should be no restriction on the support of g in this R formula.
∞ −1 0 −1 0
However,
R let φ be a function in Cc (Θ (Ω1 )) with φ = 1 on Θ (Ω0 ); then (f ◦ Θ)g =
(f ◦ Θ)φg, so one can replace g by φg in the subsequent argument. Since the map g 7→ φg
is bounded on Hs for all s, this yields the desired estimate in the end.
Page 208, line −5: ony → any
Page 210, formula (6.27): |α| ≤ k → |α| = k
Page 212, lines 9 and 10: |α| ≤ k → |α| = k
Page 218, line 2: (6.30) → (6.33)
Z Z
Page 224, line 8: (r) →
N N (r)
Page 225, line 1: if → of
Page 225, Theorem (6.47): S → ∂Ω (two places)
iθ 1
Page 227, Exercise 1: Ω should be {re : −π < θ < π, 2 < r < 1}.
Page 231, display before (7.3): ∂ α u → ∂β u
Page 235, line −6: (5.6) → (7.6)
Page 245, line −9: Put absolute value signs around the whole sum.
Page 245, lines −8 and −6: kukm,Ω → kuk2m,Ω
Page 248, lines 2 and 3 of section E: X → X
Page 272, line −7: distibution → distribution
Page 273, line 9 of proof: |α| − m + j → m − |α| + j
Page 274, line 2: φ = 1 on sing supp u → φ = 1 on a neighborhood of sing supp u
Page 280, line −7: Dξβ → Dξα
Page 287, line 9: dη → dy
Page 289, next-to-last line of proof of Corollary (8.32): Ψ−∞ → S −∞
Page 290, line 3 of proof: u(x)v(y) → u(y)v(x)
Page 293, line 4: then then → then
Page 305, line 3: and and → and
