Manuscript X-D-ST@1 · X-D-ST.tex · section · e0cf8fdb

The sharp divergence-form problem

Identification: continuous coordinates and normal flux › The sharp divergence-form problem · lines 1187–1205

Let $θ (t) = 1_{{t > 0}}$ , and put

A_{sh}^{μν} = η^{μν} + θ (t) (κ a^{μν} + κ^{2} A^{μν}) .

Extend the limiting coordinate map by

X_{sh}^{ρ} = {x^{ρ}, x^{ρ} + κ w_{0}^{ρ} + κ^{2} v_{0}^{ρ}, t < 0, t > 0.

Its positive-order positions are continuous at $Σ$ .

Displayed formulas in this passage

unlabeled · line 1190
$A_{sh}^{μν} = η^{μν} + θ (t) (κ a^{μν} + κ^{2} A^{μν}) .$
unlabeled · line 1196
$X_{sh}^{ρ} = {x^{ρ}, x^{ρ} + κ w_{0}^{ρ} + κ^{2} v_{0}^{ρ}, t < 0, t > 0.$