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du d ( du) Lu s dt d%j \ dxj for (x, 0 G o r = i2X(0, r ] , where Q is a bounded open simply connected region in E (n^2), T an arbitrary positive number, and the da are assumed only to be bounded and measurable in QT. The purpose of this note is to report results concerning the existence and certain properties of the generalized Green's function g(x0, Jo; x, t) for L subject to homogeneous boundary conditions. Our results are largely based on the maximum principle for the problem

On the Green's function for second order parabolic differential equations with discontinuous coefficients