Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations
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.
scientific article; zbMATH DE number 716203