Manuscript XIV-J@1 · XIV-J.tex · section · 1c0e72ca

Collected coefficient form

J2c: a grouped reference for the supported sector away from N › Collected coefficient form · lines 1398–1428

XIV-J@1#eq:bcoeff, XIV-J@1#eq:collected

Collect the terms of (eq:reference) with the same normal derivative. For $∣ γ ∣ \leq 3$ , put

b_{D, γ}^{\circ} = β \in N^{5} ∣ γ + β ∣ \leq 3 \sum (- 1)^{∣ β ∣} (β γ + β) v_{γ + β} c_{D, β} .

Then

t_{D}^{\circ} = ∣ γ ∣ \leq 3 \sum E_{γ} b_{D, γ}^{\circ} on U ∖ N_{U} .

The $b_{D, γ}^{\circ}$ are distributions on $S_{resp} ∖ N_{U}$ . They need not be smooth. Their complete sum may have cancellations. No coefficient is assumed nonzero or zero.

The reference estimates on compact subsets away from $N_{U}$ do not provide uniform estimates as those compact subsets approach $N_{U}$ .

Displayed formulas in this passage

XIV-J@1#eq:bcoeff · line 1402
$b_{D, γ}^{\circ} = β \in N^{5} ∣ γ + β ∣ \leq 3 \sum (- 1)^{∣ β ∣} (β γ + β) v_{γ + β} c_{D, β} .$
XIV-J@1#eq:collected · line 1412
$t_{D}^{\circ} = ∣ γ ∣ \leq 3 \sum E_{γ} b_{D, γ}^{\circ} on U ∖ N_{U} .$