Faculty of Science, Department of Mathematics, Zagazig University, Zagazig, Egypt
https://doi.org/10.1186/s42787-019-0029-6
Abstract
Consider the bi-harmonic differential expression of the form A = 2M2 + q on a manifold of bounded geometry (M, g) with metric g, where M is the scalar Laplacian on M and q ≥ 0 is a locally integrable function on M. In the terminology of Everitt and Giertz, the differential expression A is said to be separated in Lp (M), if for all u ∈ Lp (M) such that Au ∈ Lp (M), we have qu ∈ Lp (M). In this paper, we give sufficient conditions for A to be separated in Lp (M),where 1 < p < ∞
Atia, H. (2019). Separation Problem for Bi-Harmonic Differential Operators in Lp− spaces on Manifolds. Journal of the Egyptian Mathematical Society, 27(1), 1-10. doi: https://doi.org/10.1186/s42787-019-0029-6
MLA
H. A. Atia. "Separation Problem for Bi-Harmonic Differential Operators in Lp− spaces on Manifolds", Journal of the Egyptian Mathematical Society, 27, 1, 2019, 1-10. doi: https://doi.org/10.1186/s42787-019-0029-6
HARVARD
Atia, H. (2019). 'Separation Problem for Bi-Harmonic Differential Operators in Lp− spaces on Manifolds', Journal of the Egyptian Mathematical Society, 27(1), pp. 1-10. doi: https://doi.org/10.1186/s42787-019-0029-6
VANCOUVER
Atia, H. Separation Problem for Bi-Harmonic Differential Operators in Lp− spaces on Manifolds. Journal of the Egyptian Mathematical Society, 2019; 27(1): 1-10. doi: https://doi.org/10.1186/s42787-019-0029-6
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