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Layer potentials C*-algebras of domains with conical points

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Central European Journal of Mathematics

Abstract

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.

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Authors and Affiliations

  1. Instituto Superior Técnico, Math. Dept., UTL, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Catarina Carvalho

  2. Chern Institute of Mathematics, Nankai University, Tianjin, 300071, China

    Yu Qiao

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  1. Catarina Carvalho
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  2. Yu Qiao
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Correspondence to Catarina Carvalho.

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Carvalho, C., Qiao, Y. Layer potentials C*-algebras of domains with conical points. centr.eur.j.math. 11, 27–54 (2013). https://doi.org/10.2478/s11533-012-0066-y

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