Abstract
We study the Fredholm solvability for a new class of nonlocal boundary value problems associated with group actions on smooth manifolds. Namely, we consider the case in which the group action is defined on an ambient manifold without boundary and does not preserve the manifold with boundary on which the problem is stated. In particular, the group action does not map the boundary into itself. The orbits of the boundary under the group action split the manifold into subdomains, and this decomposition, being combined with the \(C^*\)-algebra techniques, plays an important role in our approach to the analysis of the problem.
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Acknowledgments
The authors wish to express gratitude to A. L. Skubachevskii for many fruitful discussions of nonlocal problems and to the anonymous referee for useful remarks.
Funding
This work was supported by the Russian Foundation for Basic Research under grant 21-51-12006 and by the Deutsche Forschungsgemeinschaft (project SCHR 319/10-1).
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Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 692–716 https://doi.org/10.4213/mzm13426.
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Baldare, A., Nazaikinskii, V.E., Savin, A.Y. et al. \(C^*\)-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators. Math Notes 111, 701–721 (2022). https://doi.org/10.1134/S0001434622050042
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DOI: https://doi.org/10.1134/S0001434622050042