Geodesic
The necessary optimality conditions for a~nonlinear stationary system whose state functional is not differentiable with respect to the control
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 32-46

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We consider a control system described by a nonlinear elliptic equation. Its control-state mapping is extended differentiable but not Gateaux differentiable for large values of the domain dimension and the nonlinearity index. We obtain a necessary optimality condition for various state functionals.
Keywords: optimal control, nonlinear elliptic equation, extended differentiability, optimality conditions. 
@article{IVM_2010_6_a3,
     author = {S. Ya. Serovaiskii},
     title = {The necessary optimality conditions for a~nonlinear stationary system whose state functional is not differentiable with respect to the control},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {32--46},
     publisher = {mathdoc},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_6_a3/}
}
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S. Ya. Serovaiskii. The necessary optimality conditions for a~nonlinear stationary system whose state functional is not differentiable with respect to the control. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 32-46. http://geodesic.mathdoc.fr/item/IVM_2010_6_a3/