Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792

CiteScore 2016: 0.80

SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125

Mathematical Citation Quotient (MCQ) 2015: 0.43

Online
ISSN
1569-3945
See all formats and pricing
More options …
Volume 19, Issue 1 (Jan 2011)

Issues

On the Cauchy problem for operators with injective symbols in the spaces of distributions

Ivan V. Shestakov
  • Institute of Mathematics, Siberian Federal University, Pr. Svobodnyi 79, 660041 Krasnoyarsk, Russia.
  • Email:
/ Alexander A. Shlapunov
  • Institute of Mathematics, Siberian Federal University, Pr. Svobodnyi 79, 660041 Krasnoyarsk, Russia.
  • Email:
Published Online: 2011-05-02 | DOI: https://doi.org/10.1515/jiip.2011.026

Abstract

Let D be a bounded domain in the n-dimensional Euclidian space (n ≥ 2) having smooth boundary ∂D. We indicate appropriate Sobolev spaces with negative smoothness in D in order to consider the non-homogeneous ill-posed Cauchy problem for an overdetermined operator A with injective symbol. We prove that elements of the indicated Sobolev spaces have traces on the boundary. This easily leads to a weak formulation of the Cauchy problem and to the corresponding uniqueness theorem. We also describe solvability conditions of the problem and construct its exact and approximate solutions. Namely, we obtain the Carleman formula recovering a vector-function u from the indicated negative Sobolev class via its Cauchy data on an open connected set Γ ⊂ ∂D and values of Au on the domain D. Some instructive examples are considered.

Keywords.: Ill-posed Cauchy problem; elliptic operators; Carleman's formula

About the article

Received: 2010-09-12

Published Online: 2011-05-02

Published in Print: 2011-05-01


Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.026.

Export Citation

Comments (0)

Please log in or register to comment.
Log in