Summary: In this note we propose a model for a nonlinear analytic problem arising as the Euler equation for minimization of a functional of norm type in Sobolev spaces of analytic functions. The principal feature of this model is the presence of an additional unknown function – a coanalytic potential – whose occurrence is caused by the fact the Lebesgue space of square-summable functions decomposes into an orthogonal sum of analytic and coanalytic subspaces. We establish that the problem is well posed. The decomposition (more precisely, its adjoint) makes it possible to give a final answer to the question of the solvability of the familiar \(\overline \partial\)-problem in the one-dimensional case. As the basic domain we restrict ourselves to the unit disk.