Manuscript III@2 · III.tex · section · 82dad3e5

Exact finite-radius boundary error

Sign, inverse, boundary, and kernel audit › Exact finite-radius boundary error · lines 2992–3006

For $x \in B_{R}$ , put

G (x, y) = - \frac{1}{4 π ∣ x - y ∣}, N_{R} f (x) = \int_{B_{R}} G (x, y) f (y) d^{3} y,

and

B_{R} [u] (x) = \int_{\partial B_{R}} (G \partial_{n} u - u \partial_{n} G) d S .

Displayed formulas in this passage

unlabeled · line 2995
$G (x, y) = - \frac{1}{4 π ∣ x - y ∣}, N_{R} f (x) = \int_{B_{R}} G (x, y) f (y) d^{3} y,$
unlabeled · line 3001
$B_{R} [u] (x) = \int_{\partial B_{R}} (G \partial_{n} u - u \partial_{n} G) d S .$