Questions on solvability of exterior boundary value problems with fractional boundary conditions

Abstract

In this paper we study questions on solvability of some boundary value problems for the Laplace equation with boundary integro-differential operators in the exterior of a unit ball. We study properties of the given integral - differential operators of fractional order in a class of functions which are harmonic outside a ball. We prove theorems about existence and uniqueness of a solution of the problem. We construct explicit form of the solution of the problem in integral form, by solving the Dirichlet problem.

Keywords

• regular harmonic function
• riemann-liouville operator
• exterior boundary value problem
• dirichlet problem