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We establish global Gaussian estimates for the Green's matrix of divergenceform, second order parabolic systems in a cylindrical domain under theassumption that weak solutions of the system vanishing on a portion of theboundary satisfy a certain local boundedness estimate and a local H\"olderestimate. From these estimates, we also derive global estimates for the Green'smatrix for elliptic systems with bounded measurable coefficients in twodimensional domains. We present a unified approach valid for both the scalarand vectorial cases and discuss several applications of our result.

Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains