...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 3 | Year 2022 | Article Id. IJMTT-V68I3P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I3P512

Boundary Value Problems for Cauchy-Riemann Systems in Some Low Dimensions


Dinh Thi Kim Nhung, Le Thi Hien, Doan Thi Linh
Abstract

In this paper we introduce some notations in Clifford algebras and boundary value problems for Cauchy-Riemann systems in ℝ𝑑with 𝑑=3,4,5,6.

Keywords
Clifford analysis, Boundary value problems, Cauchy-Riemann system.
References

[1] O. Celebi and K. Koca, A Note on a Boundary Value Problem for Nonlinear Complex Differential Equations in Wiener-type Domains, InternationalConference on Applied Mathematics, (2004) 321-326.
[2] C. Miranda, Partial differential equations of elliptic type. Ergebnisse der Mathematik and ihrerGrenzgebiete, Band 2, Springer-Verlag, New York, Second revised edition.Translated from the Italian by Zane C. Motteler. (1970).
[3] D. Gilbarg and N.S.Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag Berlin Heidelbaerg New York Tokyo (1983).
[4] Doan Cong Dinh, Dirichlet boundary value problem for monogenic function in Clifford analysis, Complex Variables and Elliptic Equations, 2014. 59 (9) (2014) 1201-1213.
[5] Doan Cong Dinh, Generalized Clifford Analysis, The doctoral thesis, Graz University of Technology, (2012).
[6] D. Alayon-Solarz and C. J. Vanegas, Operators Associated to the CauchyRiemann Operators in Elliptic Complex Numbers, Adv. Appl. Clifford Algebras. 22 (2012) 257-270.
[7] F. Brackx, R. Delanghe and F. Sommen, Clifford analysis, Pitman, Research Notes, 76 (1982).
[8] Dao Viet Cuong, From distinguishing boundaries to bounday value problems for mononegic functions, Complex Analysis and Operator Theory (2021).
[9] A. Escassut, W. Tutschke and C. C. Yang (editors),Some topicson value distribution and differentiability in complex and p-adicanalysis. Science Press Beijing. (2008).
[10] Sha Huang, Yu Ying Qiao, and Guo Chun Wen, Real and ComplexClifford Analysis, Advances in Complex Analysis and Its Applications, Springer-Verlag. 5 (2006).
[11] J. Vanegas and F. Vargas, On weighted Dirac Operators and their Fundamental Solution for Anisotropic Media, Adv. Appl. Clifford Algebras 28 (2018).
[12] V. V. Kravchenko, Applied quaternionic analysis,Research and Exposition in Mathematics, Lemgo: HeldermannVerlag.28 (2003).
[13] Le Hung Son and W. Tutschke (editors), Algebraic Structures in Partial Differential Equations Related to Complex and Clifford Analysis, Ho Chi Minh CityUniversity of Education Press, Ho Chi Minh City, (2010).
[14] Le Hung Son and W. Tutschke, Complex Methods in Higher Dimensions |Recent Trends for Solving Boundary Value and Initial Value Problems, ComplexVariables, 50 (7-11) (2005) 673679.
[15] Le Hung Son and W. Tutschke, First order Differential Operators Associated to the Cauchy-Riemann Operator in the Plane, Complex Var. Theory Appl. 48(2003) 797-801.
[16] Le Hung Son and W Tutschke,Complex Methods In Higher Dimensions - Recent Trends for Solving Boundary Value and Initialvalue Problems. Complex Variables, 50 (. 7-11) (2005) 673-679.
[17] Le Hung Son and W. Tutschke (editors), Algebraic Structures Inpartial Differential Equations Related to Complex and Clifford analysis. Ho Chi Minh City University of Education Press.Ho Chi MinhCity, (2010).
[18] Muhammad SajidIqbal, Solutions of Boundary Value Problems for Nonlinear Partial Differential Equations by Fixed Point Methods, Disseration, Graz, (2011).
[19] A.S.A. Mshimba and W. Tutschke (editors), Functional AnalyticMethods in Complex Analysis and Applications to Partial Differential Equations, Proceedings of the Second Workshop held at theICTP in Trieste, January 25-29, (1993). World Scientific (1995).3940 Bibliography
[20] Sheldon Alex, Paul Bourdon and Wade Ramey, Harmonic Function Theory,Second Edition, Springer-Verlag New York, Inc, (2001).
[21] Richard Delanghe, Clifford Analysis,History and Perspective, Computational Methods and Function Theory.1(1) (2001) 107-153.
[22] W. Tutschke, An elementary approach to Clifford Analysis. Contained in the Collection of papers [8]. (1995) 402-408.
[23] W. Tutschke, Real and Complex Fundamental Solutions - a way for Unifyingmathematical Analysis. Bol. Asoc. Mat. Venez., 9(2) (2002) 141-179.
[24] W. Tutschke, The Distinguishing Surface for Monogenic Functions in Cliffordanalysis. Advances in Applied Clifford Analysis. Online:DOI 10.1007/s00006-014-0484-y.
[25] W. E. Hamilton, Elements of Quaternion, Publisher London, Longmans, Green,& Co. (1866).
[26] W.Tutschke, Generalized Analytic Functions in Higher Dimensions, GeorgianMath. J. (2007).

Citation :

Dinh Thi Kim Nhung, Le Thi Hien, Doan Thi Linh, "Boundary Value Problems for Cauchy-Riemann Systems in Some Low Dimensions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 3, pp. 63-72, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I3P512

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved