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Title: On the Shape Gradient and Shape Hessian of a Shape Functional Subject to Dirichlet and Robin Conditions
Authors: Bacani, Jerico B.
Keywords: shape gradient
shape Hessian
Kohn-Vogelius objective functional
Dirichlet boundary value problem
Robin boundary value problem
Issue Date: 29-Jul-2014
Citation: Applied Mathematical Sciences, Vol. 8, 2014, no. 108, 5387 - 5397
Abstract: This paper focuses on minimizing a shape functional through the solution of a Pure Dirichlet boundary value problem, and a Dirichlet-Robin boundary value problem. This shape optimization problem is a variant of the Kohn-Vogelius shape optimization formulation of a Bernoulli free boundary problem. The fi rst- and second-order shape derivatives of the cost functional under consideration are explicitly derived. Interestingly, the present fi ndings coincide with the existing results regarding solutions to the Bernoulli problem.
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