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# 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

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

## Correction

Errata of paper . 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

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. 1.

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

## Author information

Correspondence to Veli B Shakhmurov. 