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Lower-semicontinuity in domain optimization problems. (English) Zbl 0629.49006
In the present paper, lower semicontinuity of certain classes of functionals is studied when the domain of integration, which defines the functionals, is not fixed. For this purpose, a certain class of domains introduced by D. Chenais [J. Math. Anal. Appl. 52, 189-219 (1975; Zbl 0317.49005)] is employed. For this class of domains, a basic lemma is proved which plays an essential role in the derivations of the lower- semicontinuity theorems. These theorems are applied to the study of the existence of the optimal domain in domain optimization problems; a boundary-value problem of Neumann type or Dirichlet type is the main constraint in these optimization problems.

MSC:
49J45 Methods involving semicontinuity and convergence; relaxation
49K20 Optimality conditions for problems involving partial differential equations
49K40 Sensitivity, stability, well-posedness
35J25 Boundary value problems for second-order elliptic equations
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