On the Mixed Dirichlet--Farwig biharmonic problem in exterior domains

Keywords: biharmonic operator, mixed Dirichlet--Farwig problem, Dirichlet integral, weighted spaces

Abstract

We study the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we study the unique solvability of the mixed Dirichlet--Farwig biharmonic problem in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight $|x|^a$. Admitting different boundary conditions, we used the variation principle and depending on the value of the parameter $a$, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions.

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Author Biography

Hovik A. Matevossian, National Research University

Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Vavilov str., 40, Moscow 119333, Russia

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Published
2019-02-28
How to Cite
Matevossian, H. A. (2019). On the Mixed Dirichlet--Farwig biharmonic problem in exterior domains. JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8322-8329. https://doi.org/10.24297/jam.v16i0.8124
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Articles