О единственности решения некоторых граничных задач для дифференциальных уравнений в области с алгебраической границей

Abstract

Classes of differential equations with constant coefficients admitting unique solutions of Dirichlet and Cauchy boundary-value problems are considered in a bounded domain with algebraic boundary. For the Dirichlet problem in a ball, the necessary and sufficient conditions for the uniqueness of the solution are obtained in the form of a countable sequence of inequalities polynomial in the coefficients of the equation.