On Dirichlet-type problems for the Lavrent'ev–Bitsadze equation

The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent'ev–Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze's terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertex.