manuscripta mathematica

, Volume 124, Issue 2, pp 139–172

The Green function estimates for strongly elliptic systems of second order

Authors

    • Mathematics DepartmentUniversity of Missouri
  • Seick Kim
    • Centre for Mathematics and its ApplicationsThe Australian National University
Article

DOI: 10.1007/s00229-007-0107-1

Cite this article as:
Hofmann, S. & Kim, S. manuscripta math. (2007) 124: 139. doi:10.1007/s00229-007-0107-1
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Abstract

We establish existence and pointwise estimates of fundamental solutions and Green’s matrices for divergence form, second order strongly elliptic systems in a domain \(\Omega \subseteq {\mathbb{R}}^n, n \geq 3\) , under the assumption that solutions of the system satisfy De Giorgi-Nash type local Hölder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to complex perturbations of a single real equation.

Mathematics Subject Classification (2000)

Primary 35A0835B45Secondary 35J45
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© Springer-Verlag 2007