On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains


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We study the unique solvability of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we prove uniqueness theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet-Steklov problem in the exterior of a compact set.

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Hovik Matevossian

Federal Research Center “Computer Science and Control”; Moscow Aviation Institute (National Research University “MAI”)

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Email: hmatevossian@graduate.org
Rússia, Vavilov str. 40, Moscow, 119333; Volokolomskoye shosse 4, Moscow, 125993

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