Layer potentials C*-algebras of domains with conical points

Catarina Carvalho ; Yu Qiao

Open Mathematics, Tome 11 (2013), p. 27-54 / Harvested from The Polish Digital Mathematics Library

Résumé

To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm conditions for the natural pseudodifferential operators affiliated to this C*-algebra.

Détail

Publié le : 2013-01-01

Zbl 1275.46054

EUDML-ID : urn:eudml:doc:269473

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