Solvability of nonlocal boundary-value problems for the Laplace equation in the ball

Abstract

In this article, we consider a class of nonlocal problems for the Laplace equation with boundary operators of fractional order. We prove the existence, uniqueness and a representation of the solutions. Also it is shown that the smoothness of solutions in Holder classes depends on the order of the boundary operators.

Keywords

• Riemann-Liouville operator
• Caputo operator
• periodic problem
• antiperiodic problem
• nonlocal problem
• Laplace equation
• Poisson kernel
• harmonic function