In this paper, the authors study an optimal control problem for quasilinear elliptic partial differential equations with pointwise state constraints. Weak and strong optimality conditions of Pontryagin maximum principle type are derived. In proving these results, we penalized the state constraints and respectively use the Ekeland variational principle and an exact penalization method.
Eduardo Casas. Jiong Min Yong. "Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic." Differential Integral Equations 8 (1) 1 - 18, 1995. https://doi.org/10.57262/die/1369143781