Solution of a Nonlocal Boundary Value Problem for the Poisson Equation with Mixed Boundary Conditions with the Use of Green's Function

摘要

In the present paper, we consider a boundary value problem with mixed boundary conditions and with a nonlocal parity condition for the Poisson equation in a half-disk. For this problem, we construct Green's function in closed form and use it to write out the solution of the original problem. Unlike [1, p. 194], we need not solve a singular integral equation to obtain the solution. We also consider other boundary conditions and write out the corresponding solutions via Green's function.