Blowup Riesz Slice Core

Pressure reconstruction and convergence bounds for the rescaled sequence.

theorem ESS.blowup_harmonic_of_mollifier_bump_pairings {U : Set CKN.Foundation.Parabolic.Vec3} (hU : IsOpen U) {Q : Set CKN.Foundation.Parabolic.Vec3} (hQ : Dense Q) {p : CKN.Foundation.Parabolic.Vec3 → ℝ} (hp : MeasureTheory.LocallyIntegrableOn p U MeasureTheory.volume) (hzero : ∀ y ∈ Q, ∀ (n : ℕ), Metric.closedBall y (CKN.sliceRadius n) ⊆ U → ∫ (x : CKN.Foundation.Parabolic.Vec3) in U, p x * CKN.spatialLaplacian (fun (z : CKN.Foundation.Parabolic.Vec3) => CKN.mollifier (CKN.sliceRadius n) ⋯ (z - y)) x = 0) : CKN.Foundation.Heat.WeaklyHarmonicOn U p

Testing the spatial Laplacian on a countable family of mollifier bumps determines distributional harmonicity on the entire open set.