Manuscript VI@1 · VI.tex · section · b5b60afb

A sourced family in the coefficient space

The linearized interface and a sourced nonempty domain › A sourced family in the coefficient space · lines 704–718

VI@1#eq:newton

The metric in Definition def:jet-space is an unknown, not an external coefficient. We next exhibit solutions in which it is nontrivially sourced.

For a spatial Schwartz source define the Newton inverse

(Δ^{- 1} b) (x) = - \frac{1}{4 π} \int_{R^{3}} \frac{b ( y )}{∣ x - y ∣} d^{3} y .

Only this inverse branch is used below.

Displayed formulas in this passage

VI@1#eq:newton · line 711
$(Δ^{- 1} b) (x) = - \frac{1}{4 π} \int_{R^{3}} \frac{b ( y )}{∣ x - y ∣} d^{3} y .$