Comparison of Green functions and harmonic measures for parabolic operators
The paper provides two-sided pointwise estimates for the Green function of a parabolic operator \[ \partial/\partial t - \text{div\,}(A(x,t)\nabla_x) + B(x,t)\cdot \nabla_x \] with real, symmetric, uniformly elliptic and Lipschitz continuous matrix \(A(x,t)\) and singular first order term over a \(C^{1,1}\)-cylindrical domain \(\Omega.\) On the base of these estimates, the author establishes equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure of the lateral boundary of \(\Omega.\)
scientific article; zbMATH DE number 2174533