Department of Mathematics
Abstract: In this talk we will discuss the asymptotic behavior of solutions to elliptic equations and parabolic equations. We will prove solutions are asymptotic to harmonic (or caloric) polynomials with both the polynomials and the error terms controlled apriorily under minimal assumptions on the coefficients. Such a decomposition can be used to study the structure of singular sets. We will show that singular sets are well approximated by hyperplanes for almost all points in singular sets.