Global Regularity and Bounds for Solutions of Parabolic Equations for Probability Measures

Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov

Given a second order parabolic operator $$Lu(t,x):=\frac{\partial u(t,x)}{\partial t}+a^{ij}(t,x){\partial }_{x_i}{\partial }_{x_j}u(t,x)+b^i(t,x){\partial }_{x_i}u(t,x),$$ we consid…