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This work deals with a non linear inverse problem of reconstructing
an unknown boundary , the boundary conditions prescribed on 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
depends only on the state
...
We prove some optimal logarithmic estimates in the Hardy space with Hölder regularity, where is the open unit disk or an annular domain of . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...
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