О Задаче Дирихле-Рикье Для Бигармонического Уравнения

We define the elementary solution of the polyharmonic equation, with the help of which an explicit representation of the Green’s function of the Dirichlet problem for the polyharmonic equation in the unit ball is given for all space dimensions except for some finite set. On the basis of the obtained Green’s function, the solution of the homogeneous Dirichlet problem in the unit ball is constructed. As an example, an explicit form of the solution of the homogeneous Dirichlet problem for the inhomogeneous polyharmonic equation with the simplest polynomial right-hand side is found.

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О Задаче Дирихле-Рикье Для Бигармонического Уравнения

Cited by 3 publications

References 21 publications

On the Green’s Function for the Third Boundary Value Problem

On the Green’s Function for the Third Boundary Value Problem

Green’s Function for the Riemann–neumann Problem for a Polyharmonic Equation in the Unit Sphere

Representation of the Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball

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