On the traces of the L2-solution of a general linear differential equation in the domain
Abstract
This paper pertains to the general theory of boundary value problems for general linear differential equations with smooth coefficients in a bounded domain with a smooth boundary and contains new advances in the general theory related to the boundary properties of solutions. Specifically, conditions on the traces of a solution to a general differential equation on the boundary of the domain are found and studied, allowing the solution to be reconstructed from its traces and the right-hand side of the equation. For the case of a general equation with constant coefficients, the resulting conditions on the traces of the solution take the form of a generalized moment problem.
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