Dirichlet-type problems for n-Poisson equation in Clifford analysis

References

• Hile GN. Hypercomplex function theory applied to partial differential equations [PhD thesis]. Bloomington: Indiana University; 1972.
   Google Scholar
• Gilbert RP, Hile G. Generalized hypercomplex function theory. Trans Am Math Soc. 1974;195:1–29.
   Web of Science ®Google Scholar
• Gilbert RP. Function theoretic methods in partial differential equations. New York: Academic Press; 1969.
   Google Scholar
• Bracks F, Delanghe R, Sommen F. Clifford analysis. London: Pitman; 1982.
   Google Scholar
• Gürlebeck K, Sprößig W. Quaternionic analysis and elliptic boundary value problems. Basel: Birkhäuser Verlag; 1990.
   Google Scholar
• Gilbert JE, Murray MAM. Clifford algebras and Dirac operators in harmonic analysis. Cambridge, UK: Cambridge Univ Press; 1991.
   Google Scholar
• Obolashvili E. Partial differential equations in Clifford analysis. Harlow: Addison Wesley Longman; 1998.
   Google Scholar
• Ryan J. Basic Clifford analysis. Cubo Math Educ. 2000;2:226–256.
   Google Scholar
• Huang S, Qiao YY, Wen G. Real and complex Clifford analysis. Springer; 2006. (Series: Advances in Complex Analysis and Its Applications; 5).
   Google Scholar
• Otto H. Cauchy-Pompeiusche integraldarstellungen in der Clifford analysis [PhD thesis]. FU Berlin; 2006.
   Google Scholar
• Begehr H, Dai DQ, Li X. Integral representation formulas in polydomains. Complex Var, Theor Appl. 2002;47:463–484.
   Google Scholar
• Begehr H, Dubinskii J. Orthogonal decompositions of Sobolev spaces in Clifford analysis. Ann Mat Pura Appl. 2002;181:55–71.
   Google Scholar
• Begehr H. Iterations of Pompeiu operators. Memoirs Differ Equ Math Phys. 1997;12:3–21.
   Google Scholar
• Begehr H. Iterated integral operators in Clifford analysis. J Anal Appl. 1999;18:361–377.
   Google Scholar
• Begehr H. Representation formulas in Clifford analysis. In: Wirgin A, editor. Acoustics, mechanics, and the related topics of mathematical analysis. Singapore: World Scientific; 2002. p. 8–13.
   Google Scholar
• Begehr H, Zhang ZX, Du J. On Cauchy-Pompeiu formula for functions with values in a universal Clifford algebra. Acta Mathematica Scientia. 2003;23:95–103.
   Web of Science ®Google Scholar
• Begehr H, Du J, Zhang SX. On higher order Cauchy-Pompeiu formula in Clifford analysis and its applications. General Math. 2003;11:5–26.
   Google Scholar
• Begehr H, Otto H, Zhang ZX. Differential operators, their fundamental solutions and related integral representations in Clifford analysis. Complex Var Elliptic Equ. 2006;51:407–427.
   Google Scholar
• Vu TNH. Integral representations in quaternionic analysis related to Helmholtz operator. Complex Variables Theor Appl. 2003;12:1005–1021.
   Google Scholar
• Begehr H. Boundary value problems in complex analysis; I. II. Bol Asoc Mat Venezolana XII. 2005;65–85:217–250.
   Google Scholar
• Aksoy Ü, Çelebi AO. Dirichlet problems for generalized n-Poisson equation. Oper Theor: Adv Appl. 2010;205:129–142.
   Google Scholar
• Begehr H. Biharmonic Green functions. Le Matematiche. 2006;LXI:395–405.
   Google Scholar
• Begehr H, Vaitekhovich T. Iterated Dirichlet problem for the higher order Poisson equations. Le Matematiche. 2008;LXIII:139–154.
   Google Scholar
• Begehr H. Six biharmonic Dirichlet problems in complex analysis. In: Le HS, editor. Function spaces in complex and Clifford analysis. Proceedings of 14th International Conference Finite Infinite Dimensional Complex Analysis and Applications; Vietnam, Hanoi: Hue University, National University Publishers; 2008. p. 243–252.
   Google Scholar
• Begehr H. Complex analytic methods for partial differential equations: an introductory text. Singapore: World Scientific; 1994.
   Google Scholar
• Begehr H, Gilbert RP. Transformations transmutations and kernel functions. Vol. I, Longman: Harlow; 1992.
   Google Scholar
• Begehr H, Gilbert RP. Transformations, transmutations and kernel functions. Vol. II, Longman: Harlow; 1993.
   Google Scholar
• Gürlebeck K, Kähler U. On a boundary value problem of the biharmonic equation. Math Meth Appl Sci. 1997;20:867–883.
   Web of Science ®Google Scholar
• Gürlebeck K, Sprößig W. Quaternionic and Clifford calculus for engineers and physicists. Chichester: John Wiley & Sons; 1997.
   Google Scholar
• Aksoy Ü. Dirichlet problem for Poisson and Bi-Poisson equations in Clifford analysis. Analysis as a life. Birkhäuser; 2019. p. 19–37.
   Google Scholar
• Zhang ZX. Integral representations and its applications in Clifford analysis. General Math. 2005;13:81–98.
   Google Scholar
• Aksoy Ü, Çelebi AO. Dirichlet problem for inhomogeneous biharmonic equation in Clifford analysis. To appear in current trends in analysis, its applications and computation. Proceedings of the 12th ISAAC Congress; Aveiro, Portugal: 2019.
   Google Scholar
• Begehr H. Integral representation in complex, hypercomplex and Clifford analysis. Integral Transf Spec Funct. 2002;13:223–241.
   Web of Science ®Google Scholar
• Kalmenov TS, Koshanov BD, Nemchenko MY. Green function representation in the Dirichlet problem for polyharmonic equations in a ball. Doklady Math. 2008;78:528–530.
   Web of Science ®Google Scholar
• Kalmenov TS, Koshanov BD, Nemchenko MY. Green function representation for the Dirichlet problem of the polyharmonic equation in a sphere. Complex Var Elliptic Equ. 2008;53:177–183.
   Web of Science ®Google Scholar
• Vekua IN. Generalized analytic functions. Oxford: Pergamon Press; 1962.
   Google Scholar