Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach

In this paper, we make use of the Sobolev space to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L ¹ spaces have natural positive cones with no interior points. The paper was written when Cuong Le Van was visiting CORE, Université catholique de Louvain, and Cagri Saglam was a research fellow of the Economics Department of the same university. The authors are indebted to an anonymous referee and Takashi Kamihigashi for very useful comments. R. Boucekkine acknowledges the support of the Belgian research programmes PAI P4/01 and ARC 03/08-302.