# 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 on 19 February 2014

## 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 $u\in {W}^{2,p}\left(0,1;E\left(A\right),E\right)$ for ${f}_{k}\in {E}_{k}$, $\lambda \in {S}_{\psi }$, with sufficiently large $|\lambda |$ and the following coercive uniform estimate holds:

$\sum _{i=0}^{2}|\lambda {|}^{1-\frac{i}{2}}{\parallel {u}^{\left(i\right)}\parallel }_{{L}^{p}\left(0,1;E\right)}+{\parallel Au\parallel }_{{L}^{p}\left(0,1;E\right)}\le M\sum _{k=1}^{2}\left({\parallel {f}_{k}\parallel }_{{E}_{k}}+|\lambda {|}^{1-{\theta }_{k}}{\parallel {f}_{k}\parallel }_{E}\right).$
(3.7)

Theorem 3.3 Assume Condition 3.2 holds. Then the operator $u\to \left\{\left(L+\lambda \right)u,{L}_{1}u,{L}_{2}u\right\}$ for $\lambda \in {S}_{\psi ,\varkappa }$ and for sufficiently large $\varkappa >0$ is an isomorphism from

Moreover, the following uniform coercive estimate holds:

$\begin{array}{c}\sum _{i=0}^{2}|\lambda {|}^{1-\frac{i}{2}}{\parallel {u}^{\left(i\right)}\parallel }_{{L}^{p}\left(0,1;E\right)}+{\parallel Au\parallel }_{{L}^{p}\left(0,1;E\right)}\hfill \\ \phantom{\rule{1em}{0ex}}\le C\left[{\parallel f\parallel }_{{L}^{,p}\left(0,1;E\right)}+\sum _{k=1}^{2}\left({\parallel {f}_{k}\parallel }_{{E}_{k}}+|\lambda {|}^{1-{\theta }_{k}}{\parallel {f}_{k}\parallel }_{E}\right)\right].\hfill \end{array}$
(3.12)

## References

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

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Correspondence to Veli B Shakhmurov.

The online version of the original article can be found at 10.1186/1687-2770-2014-43

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