On the Solvability of Exterior Boundary Value Problems for the Laplace Equation with Boundary Operator Hadamard

Yayın Aralığı: Aylık
Yayıncı: Hoca Ahmet Yesevi Uluslararası Türk-Kazak Üniversitesi

In this paper, in the class of regular harmonic functions we study the properties of some integro - differential operators, generalizing the operators of fractional differentiation in the sense of Hadamard. These operators convert regular harmonic functions in the same functions and are mutually inverse on regular harmonic functions. In the exterior of the unit ball studied the boundary value problem with the boundary operator fractional order. This problem generalizes the known Neumann problem on the boundary operators of fractional order. We prove a theorem on the existence and uniqueness of the solution of the problem. Obtained an integral representation of the solution of this problem.

Anahtar Kelimeler:

exterior problem, fractional derivative, operator Hadamard, uniqueness of the solution

On the Solvability of Exterior Boundary Value Problems for the Laplace Equation with Boundary Operator Hadamard

Keywords:

exterior problem, fractional derivative, operator Hadamard, uniqueness of the solution,

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