Asymptotic Behavior Near Zeros of Solutions of Elliptic and Parabolic Equations

Abstract

This paper discusses two aspects of local behavior of solutions of elliptic and parabolic equations, namely, polynomial asymptotics and unique continuation. Particular stress is laid on describing a new approach to these problems, by connecting to the theory of Lyapunov exponents in dynamical systems via scaling transforms. New results obtained along this line are presented with a sketch of the key ingredients of the proofs.