Mean value properties of solutions to parabolic equations with variable coefficients (Q1092326)

The main purpose of this note is to prove a result about the mean value properties of solutions of the equation \(Lu=0\), where \(L=div(A(x,t)\text{grad})-D_ t\) is uniformly parabolic operator in \(R^ n\times R_+\). The proof is based on a representation formula for solutions of the equation \(Lu=0\) involving integration on the level sets of the fundamental solution.