148
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Polyharmonic Neumann and mixed boundary value problems in the Heisenberg group

, &
Pages 1506-1518 | Received 14 Jun 2016, Accepted 23 Dec 2016, Published online: 09 Feb 2017

References

  • Kal’menov TS, Suragan D. On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation. Differ Equ. 2012;48(3):441–445.
  • Sadybekov MA, Torebek BT, Turmetov B. Representation of Green’s function of the Neumann problem for a multi-dimensional ball. Complex Var Elliptic Equ. 2016;61(1):104–123.
  • Begehr H. Orthogonal decompositions of the function space L2(D; C). J Reine Angew Math. 2002;549:191–219.
  • Karachik VV. On Solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball. J Appl Ind Math. 2014;8(1):63–75.
  • Karachik VV. On the arithmetic triangle arising from the solvability conditions for the Neumann problem. Math Notes. 2014;96(1–2):217–227.
  • Kanguzhin BE, Koshanov BD. Necessary and sufficient conditions of solvability of boundary value problems for inhomogeneous polyharmonic equation in a ball. Ufa Math J. 2010;2(2):41–52.
  • Begehr H, Vanegas CJ. Iterated Neumann problem for the higher order Poisson equation. Math Nachr. 2006;279:38–57.
  • Begehr H, Vaitekhovich T. Iterated Dirichlet problem for the higher order Poisson equation. Le Mat LXIII. 2008;139–154.
  • Celebi AO, Aksoy U. Dirichlet problems for generalized n-Poisson equations. Oper Theory Adv Appl. 2010;205:129–141.
  • Bonfiglioli A, Lanconelli E, Uguzzoni F. Stratified Lie groups and potential theory for their sub-Laplacians. Springer monograph in mathematics: Springer-Verlag, Berlin-Heidelberg; 2007.
  • David S. Jerison. The Dirichlet problem for the Kohn Laplacian on the Heisenberg group, I, J Funct Anal. 1981;43:97–142.
  • Korányi A. Poisson formulas for circular functions and some groups of type H. Sci China Ser A: Math. 2006;49:1683–1695.
  • Kumar A, Mishra MM. Polyharmonic Dirichlet problem on the Heisenberg group. Complex Var Elliptic Equ. 2008;53(12):1103–1110.
  • Dubey S, Kumar A, Mishra MM. The Neumann problem for the Kohn--Laplacian on the Heisenberg Group 𝔹n. Potential Anal. 2016;45:119–133. DOI:10.1007/s11118-016-9538-1.
  • Folland GB, Kohn JJ. The Neumann problem for the Cauchy Riemann complex. Princeton (NJ): Princeton University Press; 1972.
  • Thangavelu S. Harmonic analysis on the Heisenberg group. Boston: Birkhäuser; 1998.
  • Folland GB. A Fundamental Solution for a subelliptic operator. Bull Am Math Soc. 1973;79:373–376.
  • Korányi A. Kelvin transforms and harmonic polynomials on the Heisenberg group. J Funct Anal. 1982;49:177–185.
  • Korányi A, Riemann HM. Horizontal normal vectors and conformal capacity of spherical rings in the Heisenberg group. Bull Sci Math Ser. 1987;2(111):3–21.
  • Gaveau B. Systèmes dynamiques associés à certains opérateurs hypoelliptiques, Bull Sc Math, Paris, 2c série. T. 1978;102:203–229.
  • Korányi A. Geometric aspects of analysis on the Heisenberg group, in ‘Topics in modern harmonic analysis’. Inst Naz Alta Math, Roma. 1983. p. 209–258.
  • Greiner PC, Koornwinder TH. Variations on the Heisenberg spherical harmonics. Amsterdam: Mathematisch Centrum; 1983 ( Report ZW 186/83).

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:

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:

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.