Bulletin of the Australian Mathematical Society

Research Article

On the coercivity of elliptic systems in two dimensional spaces

Kewei Zhanga1a2

a1 School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2109, Australia

a2 Department of Mathematics, Heriot-Watt University, Riccurton, Edinburgh EH14 4AS, United Kingdom

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 xs211D2. 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.

(Received December 21 1995)