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On the coercivity of elliptic systems in two dimensional spaces

Published online by Cambridge University Press:  17 April 2009

Kewei Zhang
Kewei Zhang
Affiliation:
School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2109, Australia Department of Mathematics, Heriot-Watt University, Riccurton, Edinburgh EH14 4AS, United Kingdom
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Abstract

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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 X 2 matrices.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 423 - 430
Copyright
Copyright © Australian Mathematical Society 1996

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