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The paper concerns the study of the Pontryagin Maximum Principle for aninfinite dimensional and infinite horizon boundary control problem for linearpartial differential equations. The optimal control model has already beenstudied both in finite and infinite horizon with Dynamic Programming methods ina series of papers by the same author, or by Faggian and Gozzi. Necessary andsufficient optimality conditions for open loop controls are established.Moreover the co-state variable is shown to coincide with the spatial gradientof the value function evaluated along the trajectory of the system, creating aparallel between Maximum Principle and Dynamic Programming. The abstract modelapplies, as recalled in one of the first sections, to optimal investment withvintage capital.

Maximum Principle for Linear-Convex Boundary Control Problems applied to Optimal Investment with Vintage Capital