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Article Contents

# Second-order necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls

The first author was supported in part by NSFC grant 11371104, the second author was supported in part by NSF grant DMS-1406776.
• An optimal control problem for a semilinear elliptic equation of divergenceform is considered. Both the leading term and the semilinear term of the state equationcontain the control. The well-known Pontryagin type maximum principle for the optimal controls is the first-order necessary condition. When such a first-order necessary condition is singular in some sense, certain type of the second-order necessary condition will come in naturally. The aim of this paper is to explore such kind of conditions for our optimal control problem.

Mathematics Subject Classification: Primary: 49K20, 35J61; Secondary: 35Q93.

 Citation:

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