On Minimizing the Sum of Squares of Functional Vector Norms of Differential Operators Under Constraints.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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.
- Theoretical Mathematics