On the first-order shape derivative of the Kohn-Vogelius cost functional of the Bernoulli problem.(English)Zbl 1290.49083
Summary: The exterior Bernoulli free boundary problem is being considered. The solution to the problem is studied via shape optimization techniques. The goal is to determine a domain having a specific regularity that gives a minimum value for the Kohn-Vogelius-type cost functional while simultaneously solving two PDE constraints: a pure Dirichlet boundary value problem and a Neumann boundary value problem. This paper focuses on the rigorous computation of the first-order shape derivative of the cost functional using the Hölder continuity of the state variables and not the usual approach which uses the shape derivatives of states.
Keywords:
first-order shape derivative;Kohn-Vogelius cost functional;exterior Bernoulli free boundary problem;shape optimizationCite
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