Displaying similar documents to “A symmetry result for a fourth order overdetermined boundary value problem.”

An existence result for a quadrature surface free boundary problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2005)

Open Mathematics

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The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

Zhiming Gao, Yichen Ma, Hong Wei Zhuang (2007)

Czechoslovak Mathematical Journal

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The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.

A shape optimization approach for a class of free boundary problems of Bernoulli type

Abdesslam Boulkhemair, Abdeljalil Nachaoui, Abdelkrim Chakib (2013)

Applications of Mathematics

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We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains. ...

An existence result for an interior electromagnetic casting problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2006)

Open Mathematics

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This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.