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Minimization variational principles for linear elastodynamic, acoustic, orelectromagnetic time-harmonic waves in dissipative media were obtained byMilton, Seppecher and Bouchitt\'e generalizing the quasistatic variationalprinciples of Cherkaev and Gibiansky. Here a further generalization is made toallow for a much wider variety of boundary conditions, and in particularDirichlet and Neumann boundary conditions. In addition minimization ormaximization principles of the Hashin-Shtrikman type, incorporating"polarization fields", are developed.

Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin--Shtrikman type