Variational problems with constraints involving higher-order derivatives

V.F.Demyanov Applied Mathematics Dept., St.Petersburg State University Staryi Peterhof, St.Petersburg, 198904 RUSSIA F. Giannessi Dipartimento di Matematica, Universita di Pisa Via Buonarroti, 2, Pisa, 56127 ITALY

Abstract. The Exact Penalization approach to solving constrained problems of Calculus of Variations is extended to the case of variational problems where the functional and the constraints contain higher-order derivatives. The constraints are of the inequality type. The initial constrained problem is reduced to an unconstrained one. The related unconstrained problem is essentially nonsmooth. Nevertheless, the present state of Nonsmooth Analysis makes it possible to get proper analytical tools to overcome the arising difficulties. The main advantage of the proposed technique is its possible numerical applications for computing solutions of constrained variational problems.