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- Fourier and Mellin transform (1)
- Fourier and Mellin transforms (1)
- Fredholm property (1)
- Mellin symbols with values in the edge calculus (1)
- Operator-valued symbols (1)
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- ellipticity (1)
- manifolds with edge and boundary (1)
Institute
We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.
We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.