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.
|Number of pages
|Bulletin of the Australian Mathematical Society
|Published - Dec 1996