Quantitative uniqueness, doubling lemma and nodal sets

Friday, November 21, 2014 -
3:00pm to 4:00pm
Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property. For the first time, we investigate the quantitative uniqueness of higher order elliptic equations and show the vanishing order of solutions.  Using the Carleman estimates, we obtain the doubling estimates and optimal vanishing order of Steklov eigenfunctions, which  is the eigenfunctions of the Dirichlet-to-Neumann map. A lower bound of nodal sets of Steklov eigenfunctions is also derived.
Speaker: 
Jiuyi Zhu
Johns Hopkins
Event Location: 
Fine Hall 314