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Abstract: We construct Green-s functions for divergence form, second order parabolicsystems in non-smooth time-varying domains whose boundaries are locallyrepresented as graph of functions that are Lipschitz continuous in the spatialvariables and 1-2-H\-older continuous in the time variable, under theassumption that weak solutions of the system satisfy an interior H\-oldercontinuity estimate. We also derive global pointwise estimates for Green-sfunction in such time-varying domains under the assumption that weak solutionsof the system vanishing on a portion of the boundary satisfy a certain localboundedness estimate and a local H\-older continuity estimate. In particular,our results apply to complex perturbations of a single real equation.



Author: Hongjie Dong, Seick Kim

Source: https://arxiv.org/







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