Open Access

Erratum to: ‘Abstract elliptic operators appearing in atmospheric dispersion’ by Veli B Shakhmurov and Aida Sahmurova published in the journal of Boundary Value Problems, 2014, V. 2014: 43

Boundary Value Problems20142014:116

DOI: 10.1186/1687-2770-2014-116

Received: 1 May 2014

Accepted: 2 May 2014

Published: 14 May 2014

The original article was published in Boundary Value Problems 2014 2014:43

Correction

Errata of paper [1]. In Theorems 3.2 and 3.3 it should say m = 0 , i.e., these theorems should read as follows.

Theorem 3.2 Let Condition 3.2 hold. Then problem (3.5)-(3.6) has a unique solution u W 2 , p ( 0 , 1 ; E ( A ) , E ) for f k E k , λ S ψ , with sufficiently large | λ | and the following coercive uniform estimate holds:
i = 0 2 | λ | 1 i 2 u ( i ) L p ( 0 , 1 ; E ) + A u L p ( 0 , 1 ; E ) M k = 1 2 ( f k E k + | λ | 1 θ k f k E ) .
(3.7)
Theorem 3.3 Assume Condition 3.2 holds. Then the operator u { ( L + λ ) u , L 1 u , L 2 u } for λ S ψ , ϰ and for sufficiently large ϰ > 0 is an isomorphism from
W 2 , p ( 0 , 1 ; E ( A ) , E )  onto  L p ( 0 , 1 ; E ) × E 1 × E 2 .
Moreover, the following uniform coercive estimate holds:
i = 0 2 | λ | 1 i 2 u ( i ) L p ( 0 , 1 ; E ) + A u L p ( 0 , 1 ; E ) C [ f L , p ( 0 , 1 ; E ) + k = 1 2 ( f k E k + | λ | 1 θ k f k E ) ] .
(3.12)

Notes

Authors’ Affiliations

(1)
Department of Mechanical Engineering, Okan University
(2)
Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
(3)
Okan University

References

  1. Shakhmurov VB, Sahmurova A: Abstract elliptic operators appearing in atmospheric dispersion. Bound. Value Probl. 2014., 2014: Article ID 43Google Scholar

Copyright

© Shakhmurov and Sahmurova; licensee Springer. 2014

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.