On Minimizing the Sum of Squares of Functional Vector Norms of Differential Operators Under Constraints.

摘要

This paper considers the problem of minimizing the sum of squares of functional vector norms of differential operators under a general class of constraints. Several sufficient conditions are given for the existence of a solution. The minimization problem is shown to involve the adjoint of a naturally defined differential system with matrix coefficients. The minimizing function is characterized as the solution of a boundary value problem, in terms of the differential operator, and also the adjoint boundary value problem.