Abstract
We consider a second kind representation for solutions to a first order general uniformly elliptic linear system in a simply connected plane domain \( G \) with the \( W^{k-\frac{1}{p}}_{p} \)-boundary. We prove that the operator of the system is an isomorphism of Sobolev’s space \( W^{k}_{p}(\overline{G}) \), \( k\geq 1 \), \( p>2 \), under appropriate assumptions about coefficients and the boundary. These results are new even for solutions to the canonical first order elliptic system (generalized analytic functions in the sense of Vekua).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 542–558. https://doi.org/10.33048/smzh.2021.62.306
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Klimentov, S.B. Second Kind Representations of Sobolev Space Solutions to a First Order General Elliptic Linear System in a Simply Connected Plane Domain. Sib Math J 62, 434–448 (2021). https://doi.org/10.1134/S003744662103006X
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DOI: https://doi.org/10.1134/S003744662103006X