Geodesic
The splitting of the domain of the definition of the elliptic self-adjoint pseudodifferential operator
Journal of computational and engineering mathematics, Tome 2 (2015) no. 3, pp. 60-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work we researched domain splitting of self-adjoint elliptic pseudodifferential operator. In particular the Laplace – Beltrami operator in the space of smooth differential k-forms defined on a smooth compact oriented Riemannian manifold without boundary be such operator. This result can be used in model with Sobolev type equations.
Keywords: differential k-forms, Riemannian manifold, Sobolev type model, the direct sum of subspaces. 
@article{JCEM_2015_2_3_a5,
     author = {D. E. Shafranov},
     title = {The splitting of the domain of the definition of the elliptic self-adjoint pseudodifferential operator},
     journal = {Journal of computational and engineering mathematics},
     pages = {60--64},
     year = {2015},
     volume = {2},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2015_2_3_a5/}
}
TY  - JOUR
AU  - D. E. Shafranov
TI  - The splitting of the domain of the definition of the elliptic self-adjoint pseudodifferential operator
JO  - Journal of computational and engineering mathematics
PY  - 2015
SP  - 60
EP  - 64
VL  - 2
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JCEM_2015_2_3_a5/
LA  - en
ID  - JCEM_2015_2_3_a5
ER  - 
%0 Journal Article
%A D. E. Shafranov
%T The splitting of the domain of the definition of the elliptic self-adjoint pseudodifferential operator
%J Journal of computational and engineering mathematics
%D 2015
%P 60-64
%V 2
%N 3
%U http://geodesic.mathdoc.fr/item/JCEM_2015_2_3_a5/
%G en
%F JCEM_2015_2_3_a5
D. E. Shafranov. The splitting of the domain of the definition of the elliptic self-adjoint pseudodifferential operator. Journal of computational and engineering mathematics, Tome 2 (2015) no. 3, pp. 60-64. http://geodesic.mathdoc.fr/item/JCEM_2015_2_3_a5/

[1] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003, 216 pp. | MR | Zbl

[2] G. A. Sviridyuk, S. A. Zagrebina, “Nonclassical Mathematical Physics Models”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2012, no. 40 (299), 7–18 | Zbl

[3] F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, New York, 1983, 278 pp. | MR | Zbl

[4] D. E. Shafranov, A. I. Shvedchikova, “The Hoff Equation as a Model of Elastic Shell”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2012, no. 18 (277), 77–81 | Zbl

[5] D. E. Shafranov, “One Sobolev Type Model in the Space of Differential $k$-forms on the Sphere”, SUSU Science, Proceedings of 66th Scientific Conference of the Section of Natural Sciences (Chelyabinsk, 2014), Publishing center of SUSU, Chelyabinsk, 2014, 234–238