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

25 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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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.

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JO - Journal of Differential Equations

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Harnack Principle for Weakly Coupled Elliptic Systems

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