Quantitative uniqueness for second order elliptic operators with strongly singular coefficients


Prof. Ching-Lung Lin  ( National Cheng Kung University )

2008 - 02 - 27 (Wed.)
14:00 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk I will talk about the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a quantitative estimate of the strong unique continuation property. The proof relies on Carleman estimates with carefully chosen phases. A key strategy in the proof is to derive doubling inequalities via three-sphere inequalities. Our method can also be applied to certain elliptic systems with similar singular coefficients.