article

Title: Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in $L^p(C)$

Authors: Oliver Dragicevic and Alexander Volberg

Issue: Volume 54 (2005), Issue 4, 971-996

Abstract:

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.