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arXiv · 1007.5429

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

Sungwon Cho·Hongjie Dong·Seick Kim
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Abstract

We establish global Gaussian estimates for the Green's matrix of divergence form, second order parabolic systems in a cylindrical domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate and a local Hölder estimate. From these estimates, we also derive global estimates for the Green's matrix for elliptic systems with bounded measurable coefficients in two dimensional domains. We present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result.

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Sungwon Cho, Hongjie Dong, Seick Kim. 2010-07-30. Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains. https://doi.org/10.1007/s11118-011-9234-0

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