A general Darboux-type boundary value problem in curvilinear domains with corners for a third-order equation with dominated lower-order terms

We study solvability of the Darboux-type boundary value problem for a third-order linear partial differential equation with dominated lower-order terms. We indicate function spaces in which the problem is uniquely solvable and Hausdorff normally solvable. In the second case, the corresponding homogeneous problem is shown to have infinitely many linearly independent solutions.