Advanced search
Publication Cover
Complex Variables and Elliptic Equations
An International Journal
Volume 61, 2016 - Issue 7
Submit an article Journal homepage
53
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Integration of vector Sobolev-type PDE over octonions

Sergey V. LudkovskyDepartment of Applied Mathematics, Moscow State Technical University MIREA, av. Vernadsky 78, Moscow, Russia.Correspondence[email protected]
Pages 1014-1035 | Received 17 Feb 2014, Accepted 11 Dec 2015, Published online: 21 Feb 2016

References

  • Sveshnikov AG, Alshin AB, Korpusov MO, et al. Linear and non-linear equations of Sobolev type. Moscow: Fizmatlit; 2007.
  • Gürlebeck K, Habetha K, Sprössig W. Holomorphic functions in the plane and the n-dimensional space. Basel: Birkhäuser; 2008.
  • Gürlebeck K, Sprössig W. Quaternionic and Clifford calculus for physicists and engineers. Chichester: Wiley; 1997.
  • Gürlebeck K, Sprössig W. Quaternionic analysis and elliptic boundary value problem. Basel: Birkhäuser; 1990.
  • Ludkovsky SV. Integration of vector hydrodynamical partial differential equations over octonions. Complex Var. Elliptic Equ. 2013;58:579–609. doi:10.1080/17476933.2011.598930.
  • Ludkovsky SV. Line integration of Dirac operators over octonions and Cayley--Dickson algebras. Comp. Meth. Funct. Theory. 2012;12:279–306.
  • Ludkovsky SV. Differential equations over octonions. Adv. Appl. Clifford Alg. 2011;21:773–797. doi:10.1007/s00006-011-0286-4.
  • Ludkovsky SV. Differentiable functions of Cayley--Dickson numbers and line integration. J. Math. Sci., N.Y. (Springer). 2007;141:1231–1298.
  • Ludkovsky SV. Multidimensional Laplace transforms over quaternions, octonions and Cayley--Dickson algebras, their applications to PDE. Adv. Pure Math. 2012;2:63–103.
  • Ludkovsky SV. The two-sided Laplace transformation over the Cayley--Dickson algebras and its applications. J. Math. Sci., N.Y. (Springer). 2008;151:3372–3430.
  • Ludkovsky SV. Quasi-conformal functions of quaternion and octonion variables, their integral transformations. Far East J. Math. Sci. 2008;28:37–88.
  • Ludkovsky SV. Residues of functions of octonion variables. Far East J. Math. Sci. 2010;39:65–104.
  • Kneschke A. Differentialgleichungen und Randwertprobleme [Differential equations and boundary value problems]. Bande 1-3. Leipzig: Teubner Verlaggesellschaft; 1965.
  • Baez JC. The octonions. Bull. Amer. Math. Soc. 2002;39:145–205.
  • Kurosh AG. Lectures on general algebra. Moscow: Nauka; 1973.
  • Serôdio R. On octonionic polynomials. Adv. Appl. Clifford Alg. 2007;17:245–258.
  • Schafer RD. An introduction to nonassociative algebras. London: Academic Press; 1966.
  • Kantor IL, Solodovnikov AS. Hypercomplex numbers. Berlin: Springer-Verlag; 1989.
  • Engelking R. General topology. Berlin: Heldermann; 1989.
  • Ludkovsky SV, van Oystaeyen F. Differentiable functions of quaternion variables. Bull. Sci. Math. (Paris). Ser. 2. 2003;127:755–796.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.