Stability in shape optimization with second variation
Dambrine, Marc; Lamboley, Jimmy (2014), Stability in shape optimization with second variation. https://basepub.dauphine.fr/handle/123456789/14256
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01073089
MetadataShow full item record
Abstract (EN)We are interested in the question of stability in the field of shape optimization. Precisely, we prove that under structural assumptions on the hessian of the considered shape functions, the necessary second order minimality conditions imply that the shape hessian is coercive for a given norm. Moreover, under an additional continuity condition for the second order derivatives, we derive precise optimality results in the class of regular perturbations of a domain. These conditions are quite general and are satisfied for the volume, the perimeter, the torsional rigidity and the first Dirichlet eigenvalue of the Laplace operator. As an application, we provide non trivial examples of inequalities obtained in this way.
Subjects / Keywordsisoperimetric inequalities; shape optimization; second order sensitivity; stability in shape optimization
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