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.
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Hofmann, S., Kim, S. The Green function estimates for strongly elliptic systems of second order. manuscripta math. 124, 139–172 (2007). https://doi.org/10.1007/s00229-007-0107-1
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DOI: https://doi.org/10.1007/s00229-007-0107-1