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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 [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)

References

  1. 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.

Additional information

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

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