A relaxation result for state constrained inclusions in infinite dimension
Abstract
In this paper we consider a state constrained differential inclusion ˙ x ∈ Ax + F (t, x), with A generator of a strongly continuous semigroup in an infinite dimensional separable Banach space. Under an "inward pointing condition" we prove a relaxation result stating that the set of trajectories lying in the interior of the constraint is dense in the set of constrained trajectories of the convexified inclusion ˙ x ∈ Ax + coF (t, x). Some applications to control problems involving PDEs are given.
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