An algebra of meromorphic corner symbols |
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Authors: | L Maniccia B-W Schulze |
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Institution: | a Dipartimento di Matematica, Università di Bologna, P.zza di Porta S. Donato 5, 40126 Bologna, Italy b Institut für Mathematik, Univerität Potsdam, Postfach 601553, 14415 Potsdam, Germany |
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Abstract: | Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges. |
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Keywords: | 35J70 58J140 35S05 |
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