Integral Representations of Vector Functions Based on the Parametrix of First-Order Elliptic Systems


Otelbaev M. Soldatov A.P.
June 2021Pleiades journals

Computational Mathematics and Mathematical Physics
2021#61Issue 6964 - 973 pp.

Abstract: Generalized integrals are introduced with kernels depending on the difference of the arguments taken over a domain and a smooth contour, the boundary of this domain. These kernels arise as parametrixes of first-order elliptic systems with variable coefficients. Using such integrals (with complex density over the domain and real density over the contour), representations of vector functions that are smooth in the closed domain are described. The Fredholmity of the representation obtained in the corresponding Banach spaces is established.

bounded operator , elliptic systems , Fredholmity , parametrix , Pompeiu and Cauchy integrals

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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Federal Research Center “Informatics and Management”, Russian Academy of Sciences, Moscow, 119333, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russian Federation

Institute of Mathematics and Mathematical Modeling
Federal Research Center “Informatics and Management”
Moscow Center for Fundamental and Applied Mathematics

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