caa a22 4500 463169182 CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s10957-007-9218-9 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9218-9 Miller D. Department of Mathematics and Statistics, Wright State University, Dayton, OH, USA aut Second-Order Optimality Conditions for Constrained Domain Optimization [Elektronische Daten] [D. Miller] This paper develops boundary integral representation formulas for the second variations of cost functionals for elliptic domain optimization problems. From the collection of all Lipschitz domains Ω which satisfy a constraint ∫ Ω g(x) dx=1, a domain is sought which maximizes either $\mathcal{F}_{x_{0}}(\Omega )=F(x_{0},u(x_{0}))$ , fixed x 0∈Ω, or ℱ(Ω)=∫ Ω F(x,u(x)) dx, where u solves the Dirichlet problem Δu(x)=−f(x), x∈Ω, u(x)=0, x∈∂Ω. Necessary and sufficient conditions for local optimality are presented in terms of the first and second variations of the cost functionals $\mathcal{F}_{x_{0}}$ andℱ. The second variations are computed with respect to domain variations which preserve the constraint. After first summarizing known facts about the first variations of u and the cost functionals, a series of formulas relating various second variations of these quantities are derived. Calculating the second variations depends on finding first variations of solutions u when the data f are permitted to depend on the domainΩ. Springer Science+Business Media, LLC, 2007 Domain optimization nationallicence Second variations nationallicence Domain constraints nationallicence Optimality conditions nationallicence Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 413-432 0022-3239 134:3<413 2007 134 10957 https://doi.org/10.1007/s10957-007-9218-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9218-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Miller D. Department of Mathematics and Statistics, Wright State University, Dayton, OH, USA aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 134/3(2007-09-01), 413-432 0022-3239 134:3<413 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer