The present paper is the first in a series of works devoted to the solvability of the
Possio singular integral equation. This equation relates the pressure distribution over a
typical section of a slender wing in subsonic compressible air flow to the normal velocity
of the points of a wing (downwash). In spite of the importance of the Possio equation,
the question of the existence of its solution has not been settled yet. We provide a
rigorous reduction of the initial boundary value problem involving a partial differential
equation for the velocity potential and highly nonstandard boundary conditions to a
singular integral equation, the Possio equation. The question of its solvability will be
addressed in our forthcoming work.
