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dc.contributor.authorDambrine, Marc
dc.contributor.authorLamboley, Jimmy
dc.subjectisoperimetric inequalitiesen
dc.subjectshape optimizationen
dc.subjectsecond order sensitivityen
dc.subjectstability in shape optimizationen
dc.titleStability in shape optimization with second variationen
dc.typeDocument de travail / Working paper
dc.contributor.editoruniversityotherLMAP - Laboratoire de Mathématiques et de leurs Applications [Pau];France
dc.description.abstractenWe 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.en
dc.publisher.nameUniversité Paris-Dauphineen

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