Abstract
The theory of pseudo-differential operators (ψDO’s) on manifolds with higher-dimensional singularities (e.g. edges) was developed in [S3], [S6] in such a way that the standard elliptic (pseudo-differential) boundary value problems can be regarded as “edge problems”. In this approach the boundary is interpreted as the edge and the inner normal ℝ + as the model cone of the wedge. In this case the “wedge” is of the form ℝ + x Ω with some open set Ω ⊆ { boundary }. The idea is to perform a pseudo-differential calculus along Ω with operator-valued amplitude functions (symbols) acting in distribution spaces along ℝ +. Elements of the technique may also be found in [R2], [S3]. The point of view of boundary value problems hass been elaborated in detail also in [S4, Chapter 2].
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Schulze, BW. (1992). The variable discrete asymptotics of solutions of singular boundary value problems. In: Demuth, M., Gramsch, B., Schulze, BW. (eds) Operator Calculus and Spectral Theory. Operator Theory: Advances and Applications, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8623-9_21
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DOI: https://doi.org/10.1007/978-3-0348-8623-9_21
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