Comparison of Green functions and harmonic measures for parabolic operators

摘要

In this paper, we prove two-sided pointwise estimates for the Green function of a parabolic operator with singular first order term on a C-1,C-1-cylindrical domain Omega. Basing on these estimates, we establish the equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure on the lateral boundary of Omega. These results are first studied by some authors for certain elliptic and less general parabolic operators.