Polynomial asymptotics near zero points of solutions of general elliptic equations

We extend a classical result of Lipman Bers concerning the local behavior of solutions to a wide class of elliptic equations, systems and inequalities with singular coefficients. The main theorem states that near any zero point of finite vanishing order, the solution is asymptotic to a homogeneous polynomial solution of the “osculating” equation, under mild hypotheses on coefficients. The analysis invloves homothety blow-up arguments with the aid of some elements of Lyapunov exponents in the theory of dynamical systems.