High-contrast homogenization: #
Provider.PolynomialHomogenization.Root.CorrectorDecay.NormalizedDualToScaledNegOne
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
theorem
HCPolySupport.HighContrast.exists_scaledNegOne_pair_le_normalizedDualRows
(d : ℕ)
[NeZero d]
(s : ↑FractionalOrder)
(hsHalf : ↑s < 1 / 2)
:
∃ C < ⊤,
0 < C ∧ ∀ (n : ℤ) (F G : ↥(HilbertVectorL2 (openCubeSet (originCube d n)))) (B : ℝ),
(cubeScaleNormalizedDualNegativeBesovVectorNormTwo (originCube d n) ↑s fun (x : Vec d) => (↑↑F x).toVec) ≤ B →
(cubeScaleNormalizedDualNegativeBesovVectorNormTwo (originCube d n) ↑s fun (x : Vec d) => (↑↑G x).toVec) ≤ B →
triadicScaledNegOneNorm n F + triadicScaledNegOneNorm n G ≤ C * ENNReal.ofReal B