Definition: Laboratory support contract

The physical laboratory is

For analysis use the auxiliary flat slab

and the support tube

A supported laboratory field is a smooth field on $\hat{\mathcal{L}}$ supported in ${\mathcal{C}}_{r_{\ast }}$. It is interpreted on $I\times B_R$ through (eq:flat-chart), and is zero outside the spatial laboratory on the conical time slab.

All Cauchy data below are supported in ${\overline{B}}_{r_{\ast }}$. Newton potentials are computed on the auxiliary ${\mathbb{R}}^3$ from those declared compact sources. They are not asserted to be inverses of the global conical Laplacian.