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).
- Partial Differential Equations Seminar