Abstract
By proving a lower and an upper bound for Green's function of certain parabolic operators with Lipschitz coefficients in \(R_ + ^n \times ]0,T[,{\text{ where }}R_ + ^n = \{ x = (x_1 , \ldots ,x_n ) \in R_ + ^n :x_n > 0\} {\text{ and }}0 < T < + \infty \), we give a characterization of the associated parabolic potentials and we study in a last part the boundary behaviour of these potentials for n=1.
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Riahi, L. Green Function Bounds and Parabolic Potentials on a Half-Space. Potential Analysis 15, 133–150 (2001). https://doi.org/10.1023/A:1011230811158
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DOI: https://doi.org/10.1023/A:1011230811158