Generalized Solutions of the Linear Boundary Value Problems

Abstract

We use constructions from the general theory of boundary value problems to build a theory of generalized boundary value problems for the generalized Poisson equation. Namely, generalized solutions of various boundary value problems are introduced and studied for the matrix generalization of the Poisson equation, a description of the set of all such well-posed problems is given. The obtained results are used for advancements in the original general theory of boundary value problems.