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These notes develop the study of the Dirichlet-to-Neumann map N, associated to a domain in a compact Riemannian manifold, in a variety of situations, starting with the classical case of smoothly bounded domains, then Lipschitz domains, then rougher finite perimeter domains, and finally more exotic cases, where the boundary has a fractal character. We consider the semigroup generated by -N, as a Markov semigroup, with novel properties in the fractal case.
Course Notes and Supplementary Material (PDF format)
|Course notes||v2 PDF (504K)||10/13/21|