On the solvability of a mixed problem for the wave equation with an equivariant boundary condition

We study an equivariant mixed problem for the wave equation in a cylinder over a ball. The boundary conditions in this problem are invariant under the rotation group. The formulation considered here is the most general rotation-invariant boundary value problem in a ball, and the first, second, and third boundary value problems are its particular cases. We investigate the solvability of the problem and prove the existence and uniqueness of a generalized solution under certain assumptions on the boundary functions.