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annular domain; Poisson kernel; Hardy-Sobolev space; logarithmic estimate; Robin parameter
The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space $H^{k,\infty }$; $k \in {\mathbb {N}}^*$ of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L. Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. Math. 46 (1993), 255–269 and by S. Chaabane and I. Feki, Optimal logarithmic estimates in Hardy-Sobolev spaces $H^{k,\infty }$, C. R., Math., Acad. Sci. Paris 347 (2009), 1001–1006. As an application, we prove a logarithmic stability result for the inverse problem of identifying a Robin parameter on a part of the boundary of an annular domain starting from its behavior on the complementary boundary part.
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