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On the normal variations of a domain

D. BreschJ. Simon — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in addition that the only normal variations which preserve the regularity are those with constant magnitude. This...

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