High-contrast homogenization: Provider.PolynomialHomogenization.ConvexHardyChainMean #
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
Fractional control of means along convex ball chains #
Successive balls in a convex Hardy chain have doubling radii and quantitatively nearby centers. The fractional mean-jump estimate therefore controls each successive change of mean by the Gagliardo energy on the union of the two balls. Finite vector telescoping then compares the initial mean with the mean on the fixed core ball.
The explicit lower bound for the volume of a Euclidean ball of radius
r, obtained from the concentric ambient sup-norm ball.
Equations
- HCPolySupport.HighContrast.convexHardyBallVolumeLower d r = ENNReal.ofReal ((2 * (r / √↑d)) ^ d)