The Green function estimates for strongly elliptic systems of second order

Details The Green function estimates for strongly elliptic systems of second order The Green function estimates for strongly elliptic systems of second order

2007-04-11

arxiv.org/abs/0704.1352v2

Manuscripta Math. Vol. 124 (2007), no. 2, pp. 139-172

Mathematics

Analysis of PDEs

bibliography corrected

Scientific paper

10.1007/s00229-007-0107-1

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 H\"{o}lder 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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