| Speaker: Dr Manfred Sauter Affiliation: University of Ulm Time: 14:00 Wednesday, 18 March, 2020 Location: 303-257 |
| Abstractly the Dirichlet-to-Neumann operator is an operator that maps one type of boundary data to another type of boundary data for solutions of an elliptic partial differential equation on a domain. It has various applications from numerical analysis to spectral theory and impedance tomography. Our main focus here is to study the realisation of the Dirichlet-to-Neumann operator in the space of continuous functions on the boundary of a sufficiently regular domain. We discuss different notions of how harmonic functions satisfy Dirichlet and Neumann boundary conditions, and use these notions to provide characterisations of the Dirichlet-to-Neumann operator. For sufficiently smooth domains, we obtain a completely classical characterisation based solely on pointwise properties. Several examples highlight the sharpness of the results. This reports on joint work with Tom ter Elst. |