We study nonstandard boundary value problems of field theory for the system of Poisson equations. The feature of these problems is that the solution is looked for in subspaces that are kernels of trace operators or functionals. We establish the existence and uniqueness of a weak solution and classify the nonstandard boundary value problems under consideration.
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Yu. A. Dubinskii, “Kernels of trace operators and boundary value problems in field theory”, J. Math. Sci. 251, No. 5, 635–654 (2020).
Yu. A. Dubinskii, “Kernels of trace functionals and field-theory boundary value problems on the plane”, Proc. Steklov Inst. Math. 312, 150–161 (2021).
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Dedicated to Nina Nikolaevna Uraltseva
Translated from Problemy Matematicheskogo Analiza 127, 2024, pp. 107-116.
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Dubinskii, Y.A., Provorotova, L.V. Nonstandard Boundary Value Problems of Theory of Two-Dimensional Vector Fields. J Math Sci 281, 595–606 (2024). https://doi.org/10.1007/s10958-024-07136-7
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DOI: https://doi.org/10.1007/s10958-024-07136-7