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Estimates in the Hardy-Sobolev space of the annulus and stability result. (English) Zbl 1289.30231

Summary: 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 [J. Comput. Appl. Math. 46, No. 1–2, 255–269 (1993; Zbl 0818.65017)] and by S. Chaabane and the author [C. R., Math., Acad. Sci. Paris 347, No. 17–18, 1001–1006 (2009; Zbl 1181.46023)].
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.

MSC:

30H10 Hardy spaces
30C40 Kernel functions in one complex variable and applications
35R30 Inverse problems for PDEs
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