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2023•Baku Mathematical JournalOpen access

Solvability of boundary-value problem with bounded operator in boundary conditions for fourth-order elliptic operator-differential equation

E. S. RZAYEV

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Abstract

In the paper, we derive sufficient conditions for well-posed and unique solvability of a boundary-value problem with a bounded operator in the boundary conditions for a class of fourth-order elliptic operator-differential equations. At the same time, we make estimates for the norms of operators of intermediate derivatives closely related to the solvability conditions, which are expressed using the properties of the operator coefficients of the boundary-value problem.

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In the paper, we derive sufficient conditions for well-posed and unique solvability of a boundary-value problem with a bounded operator in the boundary conditions for a class of fourth-order elliptic operator-differential equations. At the same time, we make estimates for the norms of operators of intermediate derivatives closely related to the solvability conditions, which are expressed using the properties of the operator coefficients of the boundary-value problem.

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Available abstract

In the paper, we derive sufficient conditions for well-posed and unique solvability of a boundary-value problem with a bounded operator in the boundary conditions for a class of fourth-order elliptic operator-differential equations. At the same time, we make estimates for the norms of operators of intermediate derivatives closely related to the solvability conditions, which are expressed using the properties of the operator coefficients of the boundary-value problem.

Key concepts: Boundary value problem, Semi-elliptic operator, Mathematics, Poincaré–Steklov operator, Elliptic operator, Operator (biology), Bounded function, Differential operator

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