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Neumann and Mix Boundary Value Problems on the Upper Half Plane

Year 2022, Volume: 6 Issue: 1, 135 - 142, 31.03.2022
https://doi.org/10.31197/atnaa.950920

Abstract

We give explicit representation of Neumann boundary value problem for Bitsadze equation on the upper half plane. We will also give solution of the inhomogeneous polyanalytic equation arising from Neumann and (n-1) Dirichlet boundary conditions on the upper half plane H.

References

  • [1] H. Begehr, Boundary value problems in Complex analysis, I.F.Bol. Asoc. Mat. Venezolana V, XII, No.1(2005), 65-85.
  • [2] I.N. Vekua, Generalized analytic functions, Pergamon Press, Oxford, (1962).
  • [3] E. Gaertner, Basic complex boundary value problems in the upper half plane, PhD thesis, FU Berlin, (2006). Available at http//www.diss.fuberlin.de/diss/receive/FUDISS thesis 000000002129.
  • [4] H. Begehr, G.N. Hile, A hierarchy of integral operators. Rocky Mountain J.Math., 27 (1997), 669-706.
  • [5] A. Chaudhary, A. Kumar, Boundary value problems in upper half plane, Complex Variables and Elliptic Equations, 54 (2009), 441-448.
  • [6] A. Chaudhary, A. Kumar, Mixed Boundary value problems in the upper half plane, Journal of Applied Functional Analysis, 5(2010), 209-220.
  • [7] A. Kumar, R. Prakash, Neumann and mixed boundary value problems. Journal of Applied Functional Analysis, 3(2008), 399-418.
  • [8] H. Begehr, S. Burgumbayeva, B. Shupeyeva, Harmonic Green functions for a plane domain with two touching circles as boundary. Advanced Mathematical Models and Applications 3(2018), 18-29.
  • [9] H. Begehr, M. Akel, Neumann function for a hyperbolic strip and a class of related plane domains, Mathematis- cheNachrichten, 290 (4) (2017), 490-506.
  • [10] H. Begehr, Complex analytic methods for partial differential equations. An introductory text. World Scientific, Singapore, (1994).
Year 2022, Volume: 6 Issue: 1, 135 - 142, 31.03.2022
https://doi.org/10.31197/atnaa.950920

Abstract

References

  • [1] H. Begehr, Boundary value problems in Complex analysis, I.F.Bol. Asoc. Mat. Venezolana V, XII, No.1(2005), 65-85.
  • [2] I.N. Vekua, Generalized analytic functions, Pergamon Press, Oxford, (1962).
  • [3] E. Gaertner, Basic complex boundary value problems in the upper half plane, PhD thesis, FU Berlin, (2006). Available at http//www.diss.fuberlin.de/diss/receive/FUDISS thesis 000000002129.
  • [4] H. Begehr, G.N. Hile, A hierarchy of integral operators. Rocky Mountain J.Math., 27 (1997), 669-706.
  • [5] A. Chaudhary, A. Kumar, Boundary value problems in upper half plane, Complex Variables and Elliptic Equations, 54 (2009), 441-448.
  • [6] A. Chaudhary, A. Kumar, Mixed Boundary value problems in the upper half plane, Journal of Applied Functional Analysis, 5(2010), 209-220.
  • [7] A. Kumar, R. Prakash, Neumann and mixed boundary value problems. Journal of Applied Functional Analysis, 3(2008), 399-418.
  • [8] H. Begehr, S. Burgumbayeva, B. Shupeyeva, Harmonic Green functions for a plane domain with two touching circles as boundary. Advanced Mathematical Models and Applications 3(2018), 18-29.
  • [9] H. Begehr, M. Akel, Neumann function for a hyperbolic strip and a class of related plane domains, Mathematis- cheNachrichten, 290 (4) (2017), 490-506.
  • [10] H. Begehr, Complex analytic methods for partial differential equations. An introductory text. World Scientific, Singapore, (1994).
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Arun Chaudhary 0000-0002-7101-9679

Publication Date March 31, 2022
Published in Issue Year 2022 Volume: 6 Issue: 1

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