On Higher-Order PDE Constrained Multiobjective Optimization Models

In this paper, we formulate and prove necessary conditions of efficiency for a new class of multiobjective variational models governed by higher order partial derivatives. More precisely, we consider a multiobjective optimization model of minimizing a vector of multiple integral functionals subject to certain higher order differential equations and/or inequations. The main results are derived by applying suitable techniques coming from variational calculus. The current contribution lies in vector-valued functionals given by multiple integrals, constraint coupling, and the characterization of efficiency criteria.