Seminar series
Date
Mon, 19 Jan 2015
Time
17:00 -
18:00
Location
L4
Speaker
Angkana Ruland
Organisation
University of Oxford
In this talk I present Carleman estimates for fractional Schroedinger
equations and discuss how these imply the strong unique continuation
principle even in the presence of rough potentials. Moreover, I show how
they can be used to derive quantitative unique continuation results in
the setting of compact manifolds. These quantitative estimates can then
be exploited to deduce upper bounds on the Hausdorff dimension of nodal
domains (of eigenfunctions to the investigated Dirichlet-to-Neumann maps).
equations and discuss how these imply the strong unique continuation
principle even in the presence of rough potentials. Moreover, I show how
they can be used to derive quantitative unique continuation results in
the setting of compact manifolds. These quantitative estimates can then
be exploited to deduce upper bounds on the Hausdorff dimension of nodal
domains (of eigenfunctions to the investigated Dirichlet-to-Neumann maps).