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

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 $u\in W^{2,p}(0,1;E(A),E)$ for $f_k\in E_k$, $\lambda \in S_{\psi }$, with sufficiently large $|\lambda |$ and the following coercive uniform estimate holds:

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

(3.7)

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

$$W^{2,p}(0,1;E(A),E)\mathit{\text{ onto }}{L}^p(0,1;E)\times E_1\times E_2.$$

Moreover, the following uniform coercive estimate holds:

$$\begin{array}{c}\sum _{i=0}^2|\lambda {|}^{1-\frac{i}{2}}{\parallel u^{(i)}\parallel }_{L^p(0,1;E)}+{\parallel Au\parallel }_{L^p(0,1;E)}\hfill \\ \le C[{\parallel f\parallel }_{L^{,p}(0,1;E)}+\sum _{k=1}^2({\parallel f_k\parallel }_{E_k}+|\lambda {|}^{1-{\theta }_k}{\parallel f_k\parallel }_E)].\hfill \end{array}$$

(3.12)