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This work deals with a non linear inverse problem of reconstructing
an unknown boundary γ, the boundary conditions prescribed on γ being of Signorini type,
by using boundary measurements. The problem is turned into an optimal shape design one, by constructing
a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary.
Furthermore, we prove that the derivative of this cost function with respect to a direction θ
depends only on the state u0, and not...
Dans cet article nous prouvons un nouveau résultat d'existence pour une
classe de problèmes d'optimisation de forme assez générale. Les ouverts
que nous considérons possèdent une contrainte de nature géométrique
sur la normale intérieure. Ce travail est motivé par la formulation
variationnelle d'un problème à frontière libre dont la solution possède
cette propriété géométrique.
In this paper we consider non-compact cylinder-like surfaces called unduloids and study some aspects of their geometry. In particular, making use of a Kenmotsu-type representation of these surfaces, we derive explicit formulas for the lengths and areas of arbitrary segments, along with a formula for the volumes enclosed by them.
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