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

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://www.numdam.org/item/COCV_2001__6__73_0/} }

Arada, Nadir. Relaxation of optimal control problems in $\sf L^p$-spaces. ESAIM: Control, Optimisation and Calculus of Variations, Volume 6 (2001), pp. 73-95. http://www.numdam.org/item/COCV_2001__6__73_0/

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