Pointwise estimates using monotone rearrangements in partial differential equations were initiated by G. Talenti (using in part a technique due to V. Maz’ja) where he compared the solution of \(-\Delta \,u=f\in \,L^2_+(\Omega ), u\in H^1_0(\Omega )\) to the radial solution of \(-\Delta U\!=\!f,\,U\!\in \!H^1_0(\underset {\widetilde \ }\Omega )\) , where \(\underset {\widetilde \ }f\) is the spherical rearrangement function of f and \(\underset {\widetilde \ }\Omega \) is the ball of the same measure as \(\Omega \) .