Abstract
Starting with the Zaremba problem for the Laplacian, a boundary value problem with jumping conditions from Dirichlet to Neumann data or also with discontinuous Dirichlet- or Neumann data, a reduction to the boundary in terms of Boutet de Monvel’s calculus gives rise to an interface problem which can be interpreted as a boundary value problem on the Neumann side for the Dirichlet-to-Neumann operator. This is a first order elliptic classical pseudo-differential operator on the boundary without the transmission property at the interface. A specific choice of edge quantization admits an interpretation within the edge calculus, and we apply the formalism of the edge algebra together with interface conditions.
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