Displaying similar documents to “An existence result for an interior electromagnetic casting problem”

An existence result for a quadrature surface free boundary problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2005)

Open Mathematics

Similarity:

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.

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

Abdesslam Boulkhemair, Abdeljalil Nachaoui, Abdelkrim Chakib (2013)

Applications of Mathematics

Similarity:

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. ...

Asymptotics of an optimal compliance-location problem

Giuseppe Buttazzo, Filippo Santambrogio, Nicolas Varchon (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider the problem of placing a Dirichlet region made by small balls of given radius in a given domain subject to a force in order to minimize the compliance of the configuration. Then we let tend to infinity and look for the Γ-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.

Absolutely continuous functions of several variables and diffeomorphisms

Stanislav Hencl, Jan Malý (2003)

Open Mathematics

Similarity:

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.