High-contrast homogenization:

Provider.PolynomialHomogenization.FractionalBoundaryWeightedNearKernel

Imported from the Apache-2.0 HighContrastHomogenization development at commit 7a13dbcd8d6609264a713373f5c69ceeac870472.

Near-field fractional boundary-weight kernel

theorem HCPolySupport.HighContrast.exists_bound_lintegral_near_fractionalBoundaryKernel {d : ℕ} (hd : 1 ≤ d) {s p : ℝ} (hs : 0 < s) (hp : 0 ≤ p) (hsp : s < p) (hp1 : p < 1) : ∃ (C : ENNReal), C ≠ ⊤ ∧ ∀ (U : Set (Vec d)), IsOpenBoundedConvexDomain U → ∀ x ∈ U, ∫⁻ (y : Vec d) in U ∩ euclideanBallAt x (euclideanBoundaryDistance U x / 2), ENNReal.ofReal (euclideanDist x y ^ (s - ↑d)) * euclideanBoundaryWeight U p y ≤ C * ENNReal.ofReal (euclideanBoundaryDistance U x ^ (s - p))

Inside half the center boundary distance, Lipschitz comparability of the weight and the radius-sharp Riesz integral give homogeneous order s-p.