Novel Phenomena in Steklov Type Problems

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The main objective of this project is to study the spectra of a large class of operators which we call Steklov Type Problems; they are also known as spectral problems for Dirichlet-to-Neumann maps. These problems have connections with electrical impedance tomography, shape analysis, and image processing as well as geometric analysis, inverse problems and fluid mechanics. These problems are also very interesting from the mathematical point of view; their systematic study has started only recently and, already, a large number of unexpected phenomena have been discovered. Our project concentrates on the further investigation and discovery of these novel phenomena.