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

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.

27 pages, 0 figures

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Cited by in corpus (6)

• A Mathematical Guide to Operator Learning
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• Green's functions for elliptic and parabolic systems with Robin-type boundary conditions
• Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems
• Heat kernel for the elliptic system of linear elasticity with boundary conditions
• Green's functions for parabolic systems of second order in time-varying domains