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Biharmonic Problem with Dirichlet and Steklov-Type Boundary Conditions in Weighted Spaces

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Abstract

The uniqueness of solutions of a biharmonic problem with Dirichlet and Steklov-type boundary conditions in the exterior of a compact set are studied under the assumption that the generalized solution of this problem has a finite Dirichlet integral with a weight \({{\left| x \right|}^{a}}\). Depending on the parameter \(a\), uniqueness (non-uniqueness) theorems are proved and exact formulas for calculating the dimension of the solution space of this biharmonic problem are found.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333, Moscow, Russia

    H. A. Matevossian

  2. Moscow Aviation Institute (National Research University “MAI”), 125993, Moscow, Russia

    H. A. Matevossian

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  1. H. A. Matevossian
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Correspondence to H. A. Matevossian.

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Translated by E. Chernokozhin

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Matevossian, H.A. Biharmonic Problem with Dirichlet and Steklov-Type Boundary Conditions in Weighted Spaces. Comput. Math. and Math. Phys. 61, 938–952 (2021). https://doi.org/10.1134/S0965542521060087

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