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Open Access Correction

Correction: ‘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

Veli B Shakhmurov12* and Aida Sahmurova3

Author Affiliations

1 Department of Mechanical Engineering, Okan University, Akfirat, Tuzla, Istanbul, 34959, Turkey

2 Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

3 Okan University, Akfirat, Tuzla, Istanbul, 34959, Turkey

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Boundary Value Problems 2014, 2014:116  doi:10.1186/1687-2770-2014-116


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2014/1/116


Received:1 May 2014
Accepted:2 May 2014
Published:14 May 2014

© 2014 Shakhmurov and Sahmurova; licensee Springer.

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.

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 3.2Let 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 3.3Assume 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)

References

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