Kirichenko Y. Unique solvability of boundary value problems for general differential equations in semi-algebraic domains

The dissertation deals with the investigation of the solution uniqueness violation of boundary value problems for general partial differential equations in semi-algebraic domains. The necessary and sufficient condition of non-trivial solvability of the Dirichlet problem in a ball for ultrahyperbolic equation is obtained. The uniqueness violation criterion of the Dirichlet problem in a disk for second order differential equation with commuting matrix coefficients is proved. The uniqueness violation of the Dirichlet and “almost Cauchy” problems solutions for general differential equations in domains with angular points is considered in detail.