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

Research output: Contribution to journalArticle

13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)339-372
Number of pages34
JournalPotential Analysis
Volume36
Issue number2
DOIs
Publication statusPublished - 2012 Feb 1

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Green's Matrix
Second-order Systems
Parabolic Systems
Elliptic Systems
Estimate
Gaussian Estimates
Weak Solution
Boundedness
Divergence
Scalar
Valid
Coefficient

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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Global Estimates for Green's Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains. / Cho, Sungwon; Dong, Hongjie; Kim, Seick.

In: Potential Analysis, Vol. 36, No. 2, 01.02.2012, p. 339-372.

Research output: Contribution to journalArticle

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