Article

manuscripta mathematica

, Volume 124, Issue 2, pp 139-172

The Green function estimates for strongly elliptic systems of second order

  • Steve HofmannAffiliated withMathematics Department, University of Missouri Email author 
  • , Seick KimAffiliated withCentre for Mathematics and its Applications, The Australian National University

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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 35A08 35B45 Secondary 35J45