Space Time Test Function #
Part of the Caffarelli–Kohn–Nirenberg partial regularity proof.
def
CKN.spaceTimeTestFunction
{V : Type}
[NormedAddCommGroup V]
[NormedSpace ℝ V]
(Ω : Set Foundation.Parabolic.Vec3)
(I : Set ℝ)
:
Set (Foundation.Parabolic.Vec3 × ℝ → V)
The smooth compactly supported test-function class on Ω × I from paper label def:sws; its
ordinary product space follows the test-function convention of docs/DESIGN_NOTES.md.
Equations
- CKN.spaceTimeTestFunction Ω I = {φ : CKN.Foundation.Parabolic.Vec3 × ℝ → V | ContDiff ℝ (↑⊤) φ ∧ HasCompactSupport φ ∧ tsupport φ ⊆ CKN.spaceTimeSet Ω I}