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The Third Workshop on
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On lower semicontinuity of functionals in infinite
horizon optimal control problems
Valeria Lykina
Abstract
It is well known that a wide range of infinite horizon optimal
control problems has applications in the economic theory. In this
talk we consider consider infinite horizon optimal control
problems containing an integral functional over an unbounded
interval and where the state and control variables belong to the
weighted Sobolev and weighted $L_p$- spaces respectively.We are
interested in investigating the consequences of the
interpretation of the integral within the objective as a Lebesgue
or an improper Riemann integral. As a main result we prove a lower
semicontinuity theorem for integral functionals involving Lebesgue
integrals and provide a counterexample showing that even for a
linear functional interpreted as a Riemann improper integral the
semicontinuity fails.