Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in $L^p(C)$ Oliver DragicevicAlexander Volberg 42B2049L2530C62singular integralsquasiconformal mappingsBellman PDEstochastic optimal control We investigate a Smoluchowski equation (a nonlinear Fokker-Planck equation on the unit sphere), which arises in modeling of colloidal suspensions. We prove the dissipativity of the equation in 2D and 3D, in certain Gevrey classes of analytic functions. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2554 10.1512/iumj.2005.54.2554 en Indiana Univ. Math. J. 54 (2005) 971 - 996 state-of-the-art mathematics http://iumj.org/access/