High-contrast homogenization: Provider.Quenched.SmallContrastCorrectedEndpointCore #
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
theorem
endpoint_hcore_body_corrected_core
(d : ℕ)
(hd : 2 ≤ d)
(g : ℝ)
:
g ∈ Set.Ico 0 1 →
∃ (cSc : ℝ),
0 < cSc ∧ ∃ (alpha : ℝ) (Cdelay : ℝ),
0 < alpha ∧ 0 ≤ Cdelay ∧ ∀ (cStar gBase : ℝ) (Pbase : MeasureTheory.Measure (HCPolySupport.HighContrast.CoeffSpace d))
(Ebase : HCPolySupport.BlockMat d) (Ψbase : ℝ → ℝ) (Kbase : ℝ)
(Sbase : HCPolySupport.HighContrast.CoeffSpace d → ℝ),
cStar ∈ Set.Ioc 0 cSc →
gBase = (1 + g) / 2 →
MeasureTheory.IsProbabilityMeasure Pbase →
HCPoly.Frozen.IsStationaryLaw Pbase →
HCPoly.Frozen.IsUnitRangeLaw Pbase →
HCPoly.Frozen.CoarseEllipticityDagger Pbase gBase Ebase Ψbase Kbase Sbase →
HCPolySupport.HighContrast.annealedContrast Pbase 0 - 1 ≤ cStar →
HCPolySupport.HighContrast.blockContrast Ebase ≤ 1 + cSc →
∃ (m0 : ℕ),
3 ^ m0 ≤ (2 + HCPolySupport.HighContrast.aspectRatio Ebase * Kbase) ^ Cdelay ∧ ∀ (j : ℕ),
HCPolySupport.HighContrast.annealedContrast Pbase ↑(m0 + j) - 1 ≤ 3 ^ (-alpha * ↑j)