THE FIRST WEIERSTRASS-ERDMANN CONDITION IN VARIATIONAL PROBLEMS INVOLVING DIFFERENTIAL INCLUSIONS

摘要

In this paper, the authors continue a previous study about the broken extremals in vari-ational problems with differential inclusions. In said paper, we presented a necessary condition for extremals with corner points that is valid for shapeable sets. This condition has been obtained by adapting a novel proof of the first Weiertrass-Erdmann condition. Int he present paper we extend the class of shapeable sets and demonstrate that the set Ω := {z ∈ KC~1[a,b] | G_1(t,z(t) ≤ z'(t) ≤ G_2(t,z(t)), t ∈ [a,b] a.e.} whth G_1,G_2 ∈ C~1, is shapeable for every t. Finally, we present two examples, the second being a classic engineering problem: the optimization of hydro thermal systems.