Relaxation of optimal control problems in Lp-SPACES
UMR 5640 du CNRS, UFR MIG, Université Paul Sabatier,
31062 Toulouse Cedex 4, France; email@example.com.
Revised: 27 June 2000
Revised: 24 October 2000
We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an Lp-space (p < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
Mathematics Subject Classification: 49K40 / 49K20 / 49J20
Key words: Optimal control problems / relaxation / generalized Young measures / stability properties / Pontryagin's principle.
© EDP Sciences, SMAI, 2001