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

M. O. Otelbaev, Alexandr Pavlovich Soldatov

2021

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DOI 10.1134/s0965542521030143
Data confidence 70 medium
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Abstract

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.