Geodesic
Relaxation of optimal control problems in 𝖫 𝗉 -spaces
ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 73-95

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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an L p -space (p<∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

Classification : 49K40, 49K20, 49J20
Keywords: optimal control problems, relaxation, generalized Young measures, stability properties, Pontryagin's principle 
@article{COCV_2001__6__73_0,
     author = {Arada, Nadir},
     title = {Relaxation of optimal control problems in $\sf L^p$-spaces},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {73--95},
     publisher = {EDP-Sciences},
     volume = {6},
     year = {2001},
     mrnumber = {1804498},
     zbl = {0965.49016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COCV_2001__6__73_0/}
}
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Arada, Nadir. Relaxation of optimal control problems in $\sf L^p$-spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 73-95. http://geodesic.mathdoc.fr/item/COCV_2001__6__73_0/