On an optimal shape design problem in conduction
Mathematical Institute, University of Oxford,
24-29 St. Giles', OX1 3LB, Oxford, UK; JoseCarlos.Bellido@uclm.es
(On leave from Universidad de Castilla-La Mancha (Spain).)
In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.
Mathematics Subject Classification: 49J45 / 49Q10
Key words: Optimal shape design / relaxation / variational approach / Γ-convergence / semiconvex envelopes / quasiconvexity.
© EDP Sciences, SMAI, 2006