A Counterexample in the Theory of Coerciveness for Elliptic Systems

Abstract

ln this note we exhibition counterexample to solve an open problem presented by M. Giaquinta negatively. The problem is that if linear second order strongly elliptic systems in the sense of Legendre-Hadamard satisfy weak coerciveness condition, i. e., Garding's inequality, when the coefficients of the system are in L^∞.