High-contrast homogenization: Provider.PolynomialHomogenization.FractionalMeanOscillation

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

Fractional mean oscillation on a bounded set

Pairwise differences control the squared deviation from the volume average. On a set of bounded Euclidean diameter, inserting the fractional kernel gives the corresponding fractional Poincare estimate.

noncomputable def HCPolySupport.HighContrast.normalizedDomainMeasure {d : ℕ} (U : Set (Vec d)) : MeasureTheory.Measure (Vec d)

Volume restricted to U, with normalization factor (volume U)⁻¹.

Equations

• HCPolySupport.HighContrast.normalizedDomainMeasure U = (MeasureTheory.volume U)⁻¹ • MeasureTheory.volume.restrict U