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Boundary value problems in edge representation

✍ Scribed by Xiaochun Liu; Bert-Wolfgang Schulze

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
463 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [11]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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