caa a22 4500 445842261 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00245-010-9111-z doi (NATIONALLICENCE)springer-10.1007/s00245-010-9111-z On the Shape Sensitivity of the First Dirichlet Eigenvalue for Two-Phase Problems [Elektronische Daten] [M. Dambrine, D. Kateb] We consider a two-phase problem in thermal conductivity: inclusions filled with a material of conductivity σ 1 are layered in a body of conductivity σ 2. We address the shape sensitivity of the first eigenvalue associated with Dirichlet boundary conditions when both the boundaries of the inclusions and the body can be modified. We prove a differentiability result and provide the expressions of the first and second order derivatives. We apply the results to the optimal design of an insulated body. We prove the stability of the optimal design thanks to a second order analysis. We also continue the study of an extremal eigenvalue problem for a two-phase conductor in a ball initiated by Conca etal. (Appl. Math. Optim. 60(2):173-184, 2009) and pursued in Conca etal. (CANUM 2008, ESAIM Proc., vol.27, pp. 311-321, EDP Sci., Les Ulis, 2009). Springer Science+Business Media, LLC, 2010 First eigenvalue nationallicence Two-phase conductors nationallicence Domain variations nationallicence Dambrine M. LMAP, UMR 5142, CNRS, Université de Pau et des Pays de l'Adour, 64013, Pau, France aut Kateb D. LMAC, EA 2222, Université de Technologie de Compiègne, 60200, Compiègne, France aut Applied Mathematics & Optimization Springer-Verlag 63/1(2011-02-01), 45-74 0095-4616 63:1<45 2011 63 245 https://doi.org/10.1007/s00245-010-9111-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-010-9111-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dambrine M. LMAP, UMR 5142, CNRS, Université de Pau et des Pays de l'Adour, 64013, Pau, France aut NATIONALLICENCE 700 1- Kateb D. LMAC, EA 2222, Université de Technologie de Compiègne, 60200, Compiègne, France aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 63/1(2011-02-01), 45-74 0095-4616 63:1<45 2011 63 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer