The first eigenvalue for the -Laplacian operator.
Existence of solutions for the one-phase and the multi-layer free-boundary problems with the -Laplacian operator.
Isoperimetric inequality for an interior free boundary problem with -Laplacian operator.
Optimisation de forme et problème à frontière libre : cas du p-laplacien
An existence result for a quadrature surface free boundary problem
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.
An existence result for an interior electromagnetic casting problem
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.
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