Blowup Riesz Far Harmonic #
Pressure reconstruction and convergence bounds for the rescaled sequence.
theorem
ESS.blowup_harmonic_far_local_bound :
∃ C < ⊤,
∀ (h : CKN.Foundation.Parabolic.Vec3 → ℝ) (L R : ℝ),
0 < L →
0 < R →
R ≤ 3 * L / 4 →
MeasureTheory.MemLp h (3 / 2) MeasureTheory.volume →
CKN.Foundation.Heat.WeaklyHarmonicOn (CKN.euclideanBall 0 L) h →
MeasureTheory.eLpNorm h ⊤ (MeasureTheory.volume.restrict (CKN.euclideanBall 0 R)) ≤ C * ENNReal.ofReal (L ^ 2)⁻¹ * MeasureTheory.eLpNorm h (3 / 2) MeasureTheory.volume
A globally bounded L^(3/2) function that is harmonic on a large ball
is small on a fixed inner ball. This is the interior estimate for the far
pressure in prop:blowup-limit.