A new theory, based on the concept of formally adjoint operator, is proposed to construct a variational formulation for a linear field problem, interior or exterior, with Dirichlet, Neumann, and continuity conditions. When our result is applied to the interface problem, a useful variational expression, which competes with integral equation formulation in its capability of reducing the problem dimensionality, can be obtained. The usefulness of this novel theory is demonstrated through its application to electrostatics. Three examples are also included to confirm its validity.