The main purpose of this paper is to study the linear elliptic equation with a nonlocal condition in time. The problem is considered in an abstract Hilbert space $H$. In concrete form, the elliptic equation has been widely investigated in various applied fields, such as geophysics, plasma physics, and bioelectric field problems. Under specific assumptions on the input data, we establish the well-posedness of the solution. In the first part, we examine the regularity of the solution, and in the second part, we analyze the asymptotic behavior as certain parameters approach zero.