A nonlocal boundary problem for the Laplace operator in a half disk

Abstract

In the present work we investigate the nonlocal boundary problem for the Laplace equation in a half disk. The difference of this problem is the impossibility of direct applying of the Fourier method (separation of variables). Because the corresponding spectral problem for the ordinary differential equation has the system of eigenfunctions not forming a basis. Based on these eigenfunctions there is constructed a special system of functions that already forms the basis. This is used for solving of the nonlocal boundary equation. The existence and the uniqueness of the classical solution of the problem are proved.

Keywords

• Laplace equation
• basis
• eigenfunctions
• nonlocal boundary value problem