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

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

2010-07-30

arxiv.org/abs/1007.5429v1

Potential Analysis 36 (2012), no. 2, pp.339-372

Mathematics

Analysis of PDEs

27 pages, 0 figures

Scientific paper

10.1007/s11118-011-9234-0

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 H\"older 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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