Potential Analysis

, Volume 36, Issue 2, pp 339–372

Global Estimates for Green’s Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains


DOI: 10.1007/s11118-011-9234-0

Cite this article as:
Cho, S., Dong, H. & Kim, S. Potential Anal (2012) 36: 339. doi: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 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.


Green functionGreen’s matrixGlobal boundsSecond order parabolic systemGaussian estimate

Mathematics Subject Classifications (2010)

Primary 35A0835K40; Secondary 35B45

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsYonsei UniversitySeoulRepublic of Korea
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA
  3. 3.Department of Mathematics EducationGwangju National University of EducationGwangjuRepublic of Korea
  4. 4.Department of Computational Science and EngineeringYonsei UniversitySeoulRepublic of Korea