On the coercivity of elliptic systems in two dimensional spaces

Kewei Zhang

Research output: Contribution to journalArticle

Abstract

We establish necessary conditions for quadratic forms corresponding to strongly elliptic systems in divergence form to have various coercivity properties in a smooth domain in R2. We prove that if the quadratic form has some coercivity property, then certain types of BMO seminorms of the coefficients of the system cannot be very large. We use the connection between Jacobians and Hardy spaces and the special structures of elliptic quadratic forms defined on 2 × 2 matrices.

Original languageEnglish
Pages (from-to)423-430
Number of pages8
JournalBulletin of the Australian Mathematical Society
Volume54
Issue number3
Publication statusPublished - Dec 1996

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Coercivity
Elliptic Systems
Quadratic form
Seminorm
Hardy Space
Divergence
Necessary Conditions
Coefficient

Cite this

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abstract = "We establish necessary conditions for quadratic forms corresponding to strongly elliptic systems in divergence form to have various coercivity properties in a smooth domain in R2. We prove that if the quadratic form has some coercivity property, then certain types of BMO seminorms of the coefficients of the system cannot be very large. We use the connection between Jacobians and Hardy spaces and the special structures of elliptic quadratic forms defined on 2 × 2 matrices.",
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On the coercivity of elliptic systems in two dimensional spaces. / Zhang, Kewei.

In: Bulletin of the Australian Mathematical Society, Vol. 54, No. 3, 12.1996, p. 423-430.

Research output: Contribution to journalArticle

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PY - 1996/12

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N2 - We establish necessary conditions for quadratic forms corresponding to strongly elliptic systems in divergence form to have various coercivity properties in a smooth domain in R2. We prove that if the quadratic form has some coercivity property, then certain types of BMO seminorms of the coefficients of the system cannot be very large. We use the connection between Jacobians and Hardy spaces and the special structures of elliptic quadratic forms defined on 2 × 2 matrices.

AB - We establish necessary conditions for quadratic forms corresponding to strongly elliptic systems in divergence form to have various coercivity properties in a smooth domain in R2. We prove that if the quadratic form has some coercivity property, then certain types of BMO seminorms of the coefficients of the system cannot be very large. We use the connection between Jacobians and Hardy spaces and the special structures of elliptic quadratic forms defined on 2 × 2 matrices.

M3 - Article

VL - 54

SP - 423

EP - 430

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 1755-1633

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