Harnack Principle for Weakly Coupled Elliptic Systems

Z. Q. Chen; Z. Zhao

doi:10.1006/jdeq.1997.3300

Harnack Principle for Weakly Coupled Elliptic Systems

Z. Q. Chen^*
, Z. Zhao

^*Corresponding author for this work

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

27 Citations (Scopus)

Abstract

We prove the Harnack inequality for the weakly coupled elliptic systemS, where Su=\big (\begin{align} L_1 & & \\ & \cdots & \\ & & L_N\end{align}\big )u+Qu and u=\big (\begin{align} u_1\\ \cdot \\ \cdot \\ \cdot \\ u_N\end{align}\big ). {L_k,k=1,...,N} are second order elliptic operators with Hölder continuous coefficients andQis a matrix-valued function with singular entries. In the case thatQis irreducible, a full Harnack principle is proved.

Original language	English
Pages (from-to)	261-282
Number of pages	22
Journal	Journal of Differential Equations
Volume	139
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1997.3300
Publication status	Published - 20 Sept 1997
Externally published	Yes

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title = "Harnack Principle for Weakly Coupled Elliptic Systems",

abstract = "We prove the Harnack inequality for the weakly coupled elliptic systemS, where Su=\textbackslash{}big (\textbackslash{}begin\{align\} L\_1 \& \& \textbackslash{}\textbackslash{} \& \textbackslash{}cdots \& \textbackslash{}\textbackslash{} \& \& L\_N\textbackslash{}end\{align\}\textbackslash{}big )u+Qu and u=\textbackslash{}big (\textbackslash{}begin\{align\} u\_1\textbackslash{}\textbackslash{} \textbackslash{}cdot \textbackslash{}\textbackslash{} \textbackslash{}cdot \textbackslash{}\textbackslash{} \textbackslash{}cdot \textbackslash{}\textbackslash{} u\_N\textbackslash{}end\{align\}\textbackslash{}big ). \{Lk,k=1,...,N\} are second order elliptic operators with H{\"o}lder continuous coefficients andQis a matrix-valued function with singular entries. In the case thatQis irreducible, a full Harnack principle is proved.",

author = "Chen, \{Z. Q.\} and Z. Zhao",

year = "1997",

month = sep,

day = "20",

doi = "10.1006/jdeq.1997.3300",

language = "English",

volume = "139",

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journal = "Journal of Differential Equations",

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T1 - Harnack Principle for Weakly Coupled Elliptic Systems

AU - Chen, Z. Q.

AU - Zhao, Z.

PY - 1997/9/20

Y1 - 1997/9/20

N2 - We prove the Harnack inequality for the weakly coupled elliptic systemS, where Su=\big (\begin{align} L_1 & & \\ & \cdots & \\ & & L_N\end{align}\big )u+Qu and u=\big (\begin{align} u_1\\ \cdot \\ \cdot \\ \cdot \\ u_N\end{align}\big ). {Lk,k=1,...,N} are second order elliptic operators with Hölder continuous coefficients andQis a matrix-valued function with singular entries. In the case thatQis irreducible, a full Harnack principle is proved.

AB - We prove the Harnack inequality for the weakly coupled elliptic systemS, where Su=\big (\begin{align} L_1 & & \\ & \cdots & \\ & & L_N\end{align}\big )u+Qu and u=\big (\begin{align} u_1\\ \cdot \\ \cdot \\ \cdot \\ u_N\end{align}\big ). {Lk,k=1,...,N} are second order elliptic operators with Hölder continuous coefficients andQis a matrix-valued function with singular entries. In the case thatQis irreducible, a full Harnack principle is proved.

UR - https://www.scopus.com/pages/publications/0009183308

U2 - 10.1006/jdeq.1997.3300

DO - 10.1006/jdeq.1997.3300

M3 - Article

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SN - 0022-0396

VL - 139

SP - 261

EP - 282

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Harnack Principle for Weakly Coupled Elliptic Systems

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