Computation of sharp estimates of the Poincaré constant on planar domains with piecewise self-similar boundary (Q2031479)

This article proposes a strategy for finding sharp upper and lower numerical bounds of the Poincaré constant on a class of planar domains with piecewise self-similar boundary. The approach consists of four main components: W1) tight inner-outer shape interpolation, W2) conformal mapping of the approximate polygonal regions, W3) grad-div system formulation of the spectral problem and W4) computation of the eigenvalue bounds. The authors justifying the validity of the method and obtain general convergence estimate.