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

Imed Feki

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 481-495
  • ISSN: 0011-4642

Abstract

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The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space H k , ∞ ; k ∈ 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 , ∞ , 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.

How to cite

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Feki, Imed. "Estimates in the Hardy-Sobolev space of the annulus and stability result." Czechoslovak Mathematical Journal 63.2 (2013): 481-495. <http://eudml.org/doc/260629>.

@article{Feki2013,
abstract = {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.},
author = {Feki, Imed},
journal = {Czechoslovak Mathematical Journal},
keywords = {annular domain; Poisson kernel; Hardy-Sobolev space; logarithmic estimate; Robin parameter; annular domain; Poisson kernel; Hardy-Sobolev space; logarithmic estimate; Robin parameter},
language = {eng},
number = {2},
pages = {481-495},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimates in the Hardy-Sobolev space of the annulus and stability result},
url = {http://eudml.org/doc/260629},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Feki, Imed
TI - Estimates in the Hardy-Sobolev space of the annulus and stability result
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 481
EP - 495
AB - 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.
LA - eng
KW - annular domain; Poisson kernel; Hardy-Sobolev space; logarithmic estimate; Robin parameter; annular domain; Poisson kernel; Hardy-Sobolev space; logarithmic estimate; Robin parameter
UR - http://eudml.org/doc/260629
ER -

References

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