Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations. (English) Zbl 0817.49025

Casas, Eduardo; Yong, Jiongmin

Differ. Integral Equ. 8, No. 1, 1-18 (1995).

The authors consider an optimal control problem governed by a quasilinear operator of elliptic type. They derive an optimality system of Pontryagin’s type. The result is important in several aspects: there is no stability condition (except of course for the qualified version of the result), the operator is quite general, and the proof combines ideas of renormalization, a general lemma about approximation with functions of “small” support, and Ekeland’s principle.

Reviewer: J.F.Bonnans (Le Chesnay)

MSC:

49K20	Optimality conditions for problems involving partial differential equations
35J50	Variational methods for elliptic systems
93C20	Control/observation systems governed by partial differential equations

Keywords:

Pontryagin’s principle; quasilinear elliptic equations; optimality system; stability; Ekeland’s principle