Integral representations of solutionsof Riquier for polyharmonic equations in n-dimensional ball

The solution of Riquier’s problem - the problem of finding in n-dimensional ball of solving k + 1 - harmonic equation for given values on the boundary of the desired solution u and powers of the Laplacian from one to k inclusive of this decision is obtained. The first part provides an exact statement of the problem, the main result (form of the solution of it), and the idea of this proof is stated. The second part introduces a family of some differential and integral operators in the space of harmonic functions in the ball used in the proof of the main result; some properties of these operators are set. The content of the third part is the proof of the main result. It is based on the properties of operators introduced in the second part.

differential equations, polyharmonic equation, polyharmonic functions, biharmonic equation, boundary value problems, the problem of Riquier for a polyharmonic equation