| Abstract: |
| We study Green`s matrices for non-divergence form parabolic systems in cylindrical domains. Green`s matrices play an important role in studying parabolic systems. When the coefficients are sufficiently smooth, say H\"{o}lder continuous, then the existence and pointwise estimates of Green`s matrices are well established. However, when the coefficients are merely continuous, then Green`s matrices do not necessarily exist as functions. We show that when the mean oscillation of the coefficients satisfies the Dini condition, then the Green`s matrices exist. We also establish the Gaussian bounds for the Green`s matrices. This work presents a unified approach valid for both the scalar and vectorial cases. |
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