Estimates in the Hardy-Sobolev space of the annulus and stability result

Title:

Estimates in the Hardy-Sobolev space of the annulus and stability result

Creator:

Feki, Imed

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:33520747-e6fb-47d7-b9c1-8766fc7a54e9
uuid:33520747-e6fb-47d7-b9c1-8766fc7a54e9

Subject:

annular domain, Poisson kernel, Hardy-Sobolev space, logarithmic estimate, and Robin parameter

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

481-495

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false