Jenn-Nan Wang (National Taiwan University) March 17 2011 |

Lecture 1. 11:00-11:50, 5E102

Title: Carleman estimates and quantitative uniqueness estimates I

Abstract: In this lecture, I would like to review some interesting applications of quantitative uniqueness estimates in inverse problems. The main part of the lecture is to derive doubling inequalities for the second order elliptic equation with lower order terms having sharp radially symmetric singular coefficients.

Lecture 2. 1:00-1:50, 5E102

Title: Carleman estimates and quantitative uniqueness estimates II

Abstract: In this lecture, I will discuss the strong unique continuation property for the Lame system with rough coefficients. The result is in a quantitative form in the sense that we derive a lower bound of the vanishing rate at one point for any nontrivial solution of the Lame system.

Lecture 3. 3:00-3:50, 5E102

Title: Carleman estimates and quantitative uniqueness estimates III

Abstract: Using the techniques in proving three-ball inequalities, I would like to discuss how to derive a minimal decay rate at infinity for any nontrivial velocity function of the stationary Navier-Stokes equation.