Optimal logarithmic estimates in the Hardy–Sobolev space of the disk and stability results

We prove a logarithmic estimate in the Hardy–Sobolev space Hk,2, k a positive integer, of the unit disk D. This estimate extends those previously established by L. Baratchart and M. Zerner in H1,2 and by S. Chaabane and I. Feki in Hk,∞. We use it to derive logarithmic stability results for the inver...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 395; no. 1; pp. 366 - 375
Main Authors:	Feki, I., Nfata, H., Wielonsky, F.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-11-2012 Elsevier
Subjects:	Classical Analysis and ODEs Hardy–Landau–Littlewood inequality Hardy–Sobolev space Inverse problem Logarithmic estimate Mathematics Stability Hardy–Landau–Littlewood inequality Hardy–Sobolev space Stability Logarithmic estimate Inverse problem
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We prove a logarithmic estimate in the Hardy–Sobolev space Hk,2, k a positive integer, of the unit disk D. This estimate extends those previously established by L. Baratchart and M. Zerner in H1,2 and by S. Chaabane and I. Feki in Hk,∞. We use it to derive logarithmic stability results for the inverse problem of identifying Robin’s coefficients in corrosion detection by electrostatic boundary measurements and for a recovery interpolation scheme in the Hardy–Sobolev space Hk,2 with interpolation points located on the boundary T of the unit disk.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2012.05.055