The Green function estimates for strongly elliptic systems of second order

Steve Hofmann; Seick Kim

doi:10.1007/s00229-007-0107-1

The Green function estimates for strongly elliptic systems of second order

Steve Hofmann^*, Seick Kim

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

108 Citations (Scopus)

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 Ω ⊆ ℝⁿ, n ≥ 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.

Original language	English
Pages (from-to)	139-172
Number of pages	34
Journal	Manuscripta Mathematica
Volume	124
Issue number	2
DOIs	https://doi.org/10.1007/s00229-007-0107-1
Publication status	Published - Oct 2007

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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 Ω ⊆ ℝn, n ≥ 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.",

author = "Steve Hofmann and Seick Kim",

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T1 - The Green function estimates for strongly elliptic systems of second order

AU - Hofmann, Steve

AU - Kim, Seick

PY - 2007/10

Y1 - 2007/10

N2 - We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain Ω ⊆ ℝn, n ≥ 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.

AB - We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain Ω ⊆ ℝn, n ≥ 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.

UR - https://www.scopus.com/pages/publications/34548640154

U2 - 10.1007/s00229-007-0107-1

DO - 10.1007/s00229-007-0107-1

M3 - Article

SN - 0025-2611

VL - 124

SP - 139

EP - 172

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 2

ER -

The Green function estimates for strongly elliptic systems of second order

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