http://dspace.upb.edu.ph/jspui/handle/123456789/35 On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem Bacani, Jerico B.; Peichl, Gunther 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 H¨older continuity of the state variables and not the usual approach which uses the shape derivatives of states. 2013-11-01T00:00:00Z http://dspace.upb.edu.ph/jspui/handle/123456789/34 Another Class of Admissible Perturbations of Special Expressions Bacani, Jerico B. 2014-01-01T00:00:00Z http://dspace.upb.edu.ph/jspui/handle/123456789/33 On the Shape Gradient and Shape Hessian of a Shape Functional Subject to Dirichlet and Robin Conditions Bacani, Jerico B. 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. 2014-07-29T00:00:00Z